Very old post, but I thought I'd chime in, in case my knowledge and research can help someone. In the UK, for example, I believe a Master of Computer Science is, wait for it, an undergraduate master's degree, as opposed to a graduate master’s degree. And 21 terms after matriculation, just like some other master’s degrees, they are elevated to MA status, like the BA. The UK system is complicated as there are also graduate bachelor's degrees. The difference seems to be that bachelors were broader, masters are more specific, and doctorates are beyond a master's in order of specific study and depth.
In the United States, in contrast, the Juris Doctorate used to be called the Bachelor of Laws and was an undergraduate degree. They elevated it to doctoral status based on how much work and study was put in to achieve it, but it is not equivalent to a research doctorate. It is often called a first professional degree, and technically ranks below a master's degree. The de facto master's degree in law in the United States is the Master of Laws, LLM or MLL. Beyond that is the JSD, Doctor of Juridical Science, and in the US, it is equivalent to the PhD. Other American doctorates equivalent to the JSD and PhD (in that they are research doctorates and hold the same prestige) include the Doctor of Business Administration (DBA) and Doctor of Engineering (DEng). However, if you read this article: https://en.wikipedia.org/wiki/Degrees_of_the_University_of_Oxford
you will see that a PhD is one of the lower ranking doctorates, as is the DEng. There is even an MEng that is considered an undergraduate degree, because it has the specific scope of study, but not the depth or rigor of a graduate degree. Another example where the US and UK differ is the MD, or Doctor of Medicine. The MD is the US is a first professional degree, and not a research doctorate, and ranks below the PhD and even a master's (academically). However, in the UK, the MD is one of the highest doctorates attainable. Another high doctorate, the Doctor of Science (DS) ranks very high in the UK and in some universities in Europe the DS and other doctorates or their equivalents are considered higher doctorates for beyond PhD research or in recognition of great contributions to the field of science. The DBA either does not exist in the UK, or is not prevalent, same as the Doctor of Arts (DA). Traditionally, the MBA is a terminal degree and no research degree or other degree in business is more advanced than an MBA, but the US invented the DBA as a PhD equivalent for people who wanted to do research, and there are others, such as the Doctor of Management, called a DM in the US to not confuse it with an MD, although in Europe and New England, an MD can also be referred to as a DM, adding to the confusion.
When it comes to Science and Computer Science, at the master’s level, which is always graduate level in the United States, unlike a doctorate, which can sometimes be professional (MD, JD...) and rank below a research doctorate (PhD, DBA, DS), they are the same level: master's. The difference is that the MCS is a professional master's degree for those wanting careers while an MS is in preparation for a PhD. Often, an MCS requires additional coursework and a project, while an MS student tries to practice research for the PhD. Given this, an MCS is superior to an MS if you do not intend to pursue a PhD. If you do want to pursue a PhD, the MS prepares you for that course of study, however, the MCS teaches you more things, so they both accelerate you, just in different ways.
For US study, if you visit https://www2.ed.gov/about/offices/list/ous/international/usnei/us/edlite-structure-us.html
you will see that there are six levels of education, from lowest to highest (I also give examples): associate (AA, AAS, AS), bachelor (BA, BFA, BS), first professional (JD, MD), master (MCS, MS, MBA), advanced intermediate (Post-Graduate Certificate), and research doctorate (PhD, DBA, DS). Notice how the Doctor of Computer Science is not on that list of research doctorates. However, if you find a program offering a DCS, you assume it is higher than an MCS. More complications if you try to draw relations: some schools offer a JM or MJ, a Master of Jurisprudence. Some might think that is below a JD, but the JD used to be a bachelor's and was elevated to a first professional, which would make the MJ like a bachelor's, but all master's degrees in the US are graduate degrees.... The MJ is considered by some schools as equivalent to the MLL and focuses on learning law for people who are involved in law but are not lawyers. So technically, academically it is higher and a JD (formerly the BLL) BUT does not prepare you for the lawyer profession and does not enable you to pass the bar. In more ancient times, master and doctor were used interchangeably. It seems doctor is used for those who are prepared for the profession or have professional experience whereas a master is used for someone with great knowledge and academic achievement, regardless of professional experience. But then what is a professional master's degree? An example is an MBA and I've heard it be called a second professional degree. Since it is a terminal degree, some people consider it higher than a normal master's degree, and traditionally, there was no DBA, so it was like a doctorate, without the distinction of a doctorate, in that field. So here we see doctor being a distinction, not a higher level of academic study. Think about it this way, a RESEARCH doctorate is a master's degree where you are generally paying to do research at a school instead of being paid to do research. But not everyone wants to be a researcher. Also, in the US, a research doctorate typically requires more course work. So, therefore the Doctor of Computer Science is considered higher than a Master of Computer Science because it requires more coursework but is not considered to be at the same level of a PhD, according to the US Department of Education. So, it is a strange degree that is in between a master's and a research doctorate, according to them. It is the fifth level, according to them: advanced intermediate, a level that offers certificates, diplomas, and even degrees. Why did I go so much in depth and talk about doctorates? Because while a DSC (Doctor of Computer Science) is considered lower than a PhD, for master's level, the amount of coursework is slightly more, and any research done by an MS student is just an introduction into professional research that will be done by a PhD. There is no prestige in MS research, it is just a substitute, and therefore in the US, academically, an MS is equivalent to an MCS. And the name MS is sometimes misleading, as there are schools in the US that offer an MS without requiring a thesis, instead wanting projects or just coursework, making them an American MCS but keeping the traditional MS name. Globally, MS is recognized as higher than an MCS, but in the UK, an MCS (undergrad) is later elevated to MA status after so many terms, and therefore after so many terms and maturing the MCS holder will be considered an MA, which is higher than an MS in the UK. In the US, they hold the same rank academically, but are geared towards different goals, in the same way an MS in Electrical Engineering is for careers in electronics while an MS in Biology is for going into biological research, medicine, or pursue an MD or PhD. I have not seen any DCS in the UK, but it is likely they would not hold any higher ranking than an MA, the same as an MCS. So, the DCS is a bit higher than an MCS, but the difference is considered negligible and in the UK is not recognized, as they would say the MCS matures to MA status, the DCS does not exist, but I assume they would think they just mature faster to an MA level of study. If you read the Wikipedia article, you will see that MA is held to an extremely high level of respect, and only the DD and DCL hold more prestige if the holder only has one degree. I think the only mistake in the Wikipedia article is that the BD (Bachelor of Divinity) is considered higher than the PhD but is not listed in the right place.
Lastly, I have seen DCS programs that require many more units than some PhDs. Some PhDs I have seen require the same if not less credit units than a master's degree but just add research and dissertation, which further emphasizes that doctorates are degrees for those in practice, while a master's degree is solely academic achievement. This contradicts the US Department of Education, as some level 5 degrees are potentially superior to level 6, depending on the school and program. And if you want to be an actual doctor like a medical physician or a lawyer, the JD and MD are superior, but also having a PhD will make you a more knowledgeable and capable professional. Different names, different worth for different things.
To sum it up, if you plan to study and work in the US, the MCS is just as good as an MS, especially if you do not plan to pursue a research doctorate. If you plan to study or work overseas, the MS translates more to what the US graduate program represents. If you want to get a PhD in the US, either should work, but you should check with the school you want to attend. If you plan on getting a doctorate and want international recognition, a PhD or DS is better, but if you stay in the US, a DCS may essentially be the same. Countries are trying to standardize things to match up, but there are still some differences. Last examples, a licentiate in Europe is a master's degree level or higher award to prepare someone for a profession, and sometimes is considered higher than a master's degree (like an MBA) but below a doctorate, depending on the country. Look up "Higher Doctorate" on Wikipedia, and you will see countries like France, Russia, and Germany offering either degrees or distinctions beyond a doctorate. There used to be something called ISCED level 9, but it was removed.
Other sources: Personal research and experience