I am a physics undergrad, and plan to pursue a PhD in mathematical physics (string theory?). I have heard from a lot of people, who have personally seen the research scenario at universities both in the US and Europe, that it is much easier to get a PhD from a European university, that it takes about 3-4 years in a good university in Europe, while more than 5 years in American universities. Another thing I have been told is that in Europe you get your PhD after 4 years atmost by default, even if you have not done any original research. Is it true?
Short answer: No. Long answer: Determining the minimum bar for which a PhD can be awarded is a bad exercise. If you are merely working towards the minimum you will not successfully complete a PhD.
One thing to note is that PhDs in the US tend to be open ended (to the extent you can continue to get funding) while in Europe they tend to have fixed durations. This means in Europe the bar comes whether you are ready or not while in the US you get to chose when you defend. Neither is easier, just different.
The duration between US and Europe are not usually the same, mostly because in the US, you only need to have a Bachelor degree to enrol for a PhD (and you can get a Master during the PhD), while in Europe, it's usually required to have a Master degree before enrolling for a PhD. Since it can take two years to get a Master, you also need about 5 years after your Bachelor to get your PhD.
I don't know if you always get your PhD after a number of years, no matter what, but the point in Europe is that a PhD is not necessarily an advantage on the market, with respect to a Master (at least, that's true in France), and is mostly required for working in Academia. In Academia, nobody cares that you have a PhD (because, well, almost everybody got one), so your publications, references, contacts, your CV in general will make a difference, not your degree. Hence, it might be possible that you can get the degree after a while, knowing that it's useless anyway if you haven't done any original research (although in many places, it's now required to have a given number of publications before being able to submit a PhD thesis). But I wouldn't claim in any way that it's a common practice, and I know several persons who have dropped (or been suggested to drop ...) their PhD program.
As for your main question, I don't know if one can tell whether it's easier to get a PhD in Europe than in the US, because it's hard to define what is "easier". If your question is whether you can come to Europe, enrol to any PhD, just wait 4 years and get your PhD, the answer is no.
Remember that Europe is a big place, comprised of lots of different countries. It doesn't make sense to talk about a European "PhD". The mechanism and typical PhD lengths between countries can be completely different.
The next few comments relate to the UK PhD system.
You don't get a PhD automatically after 4 years. I can introduce you to a few people who will testify to this!
In the UK, a PhD doesn't involve a "taught" aspect. I believe that in the US, the first two(?) years typically involve examinations.
In most Universities I'm familiar with, PhD students do not have a heavy teaching load. In my department, PhD students are allowed to take some tutorials/marking for additional money, but this is on top of there usual PhD working week. The number of hours a PhD student can work is closely monitored. In particular, it's incredibly rare for a PhD student to take undergraduate lectures.
I believe it is common in the US for PhD student to run a lecture course.
There are tough (read respectable) and relatively easy (read weaker) schools and PhD programs in both sides. You could find a comparatively easy US university v.s. top school in Europe, and vice versa.
I suggest to set your goals a bit higher than you think you can reach rather than wasting time (read life) shooting for an "easy" PhD track.
I have had the pleasure of both systems, US and European. The simple fact is that the average PhD takes less time in Europe than in the US. This does not directly correlate to quality (Although I have a somewhat informed opinion about that which I'll offer later), merely time to completion. Most of this has to due with the differences in Bachelor degrees from the 2 regions, commonly only 3 years in Europe, 4 in the US. Masters are also treated differently in both locations.
The real issue in my opinion is the lack of options for EU students. Both the US and Europe are experiencing a "watering-down" of the PhD, since they are all but required in so many places where they add no value other than haughty title. This is markedly worse in Europe, but the US is doing everything it can to "catch-up." In the US, the better job market allows multiple paths to success if you'd like to forego the PhD, while avoiding an advanced degree in Europe condemns one to worse underemployment than is already seen there (read that a Masters(Europe) is a Bachelors(US)).
Frankly, people want to believe their PhDs were exceptional and that by extension they endow their holders with exceptionality, but this is not true. A prerequisite PhD is a symptom of a sluggish, un-dynamic labor market, that sentences you to underpay for 3-5 years. If you really think you need one, the best advice is to find an advisor you can work with (a lot of them are amoral tyrants) finish it as quickly as possible, and move on. Contrary to statements above, what you get out is not linked exclusively to what you put in, and there are some very easy ones available.
Which country in the EU is that one supposed to be? In Portugal to enter a PhD program you either need to have a Masters or an exceptional Bachelors with high marks and letters of recommendation from senior researchers (only accepted in cases where applicants already have a publication record). A PhD usually takes around 5 years to complete. Exceptional people may do it in 4 years and quite a lot of students take 6 years or more to get one.
You do not get a PhD without a solid publication record. The requirements vary by institution and may include the number of publications and the impact factor of the publications.
If you are not motivated to spend a considerable amount of time studying that subject you should not bother getting the PhD. Also like others have said the career prospects and financial gains are not worth it either during the PhD or for the first 5 years after the PhD. Even then your position is not ensured. A leading academic researcher with that kind of income will be someone who is good at bringing research funding. Those kinds of people would manage just as well or better financially in the private sector.