I've worked in the field of research administration in the US for nearly 15 years, with more than half at an R1 institution, and I am a member of NCURA, where I have learned about the practices of many institutions across the US. I can tell you that first of all, you are unlikely to be able to find published information on this question with great detail due to confidentiality of this information, even within an institution, let alone information open to the public. However, I can give you the benefit of my experience, with the hope that it may give you some insights on how different types of people can approach funding given their circumstances.
Looking at major US federal sponsors and how they function can reveal some key behaviors by field:
As mentioned in a comment, the medical fields in the US are generally required to do a large amount of fundraising to pay for their base salary. The medical fields also rely primarily on NIH, which have specific rules that create an environment that the medical field must react to. Specifically, NIH requires investigators to commit time on projects if listed as senior/key personnel, but also caps their salary. This creates a situation where PIs need hard money to cover time on NIH projects, and soft money is also not going to be infinitely generous to pay for a large portion of one's salary, so many grants would be needed. Some folks therefore ask for slivers of time on a host of projects. This means that no individual project becomes as important, of course. There are going to be cases where there are large center projects that demand much larger portions of time, e.g. as much as 2 months. As you can imagine, there is a lot of applied and basic research funded by NIH. In 2016, their blog post showed the split being nearly 50-50.
NSF is the primary US federal sponsor that is associated with basic research. Unfortunately it is a joke among faculty that NSF actually stands for "Not Sufficiently Funded". If you look at the NSF report that was recently released on how US R&D expenditures look from 1970-2021, you will find that basic research is always the least funded type of research in the US. This is obviously somewhat disappointing when some areas of study depend so deeply on basic research. As the report goes on to say, 41% of basic research in 2020 was federally funded, whereas industry funds 91% of funding for development and 59% of applied research. NSF is recently soliciting more funding from industry to help fund their endeavors. These jointly-funded solicitations can in some cases result in awards with a mix of a federal grant and gift-like funding from industry.
DOD frequently relies on relationship building in order to generate a portfolio of DOD funding. Some institutions will have policies against development projects; some against confidential research, which development research may require. You will notice that where business is the leading entity doing this research, they are more likely to do confidential research (hence the concept of DOD contractors). Often in sponsored research, academic institutions will take a tiny piece off a development project to perform basic research. This allows them to take funding from sponsors that may otherwise be unavailable due to institutional research policies--a key example being DARPA, which is mostly found at engineering schools.
Thus with these large funding mechanics in play, the remaining question -- the ability to do research freely, means that non-sponsored funding lets you pick what your endeavor is "without restriction". What does "restriction" mean? For some folks that is the specific policies of a sponsor they normally do business with -- e.g. a salary cap with NIH. Does this non-sponsored funding allow new cost categories without restrictions, e.g., staff members, alcohol? Most people pursue non-sponsored funding because it is going to be easier to use, but also because it can be less competitive depending on how it is procured -- relationships, smaller awards with higher success rates, etc. Internal funding is generally less demanding on administration because it's all done within the institution and some institutional norms are used as a default. As collaborations become the norm in sponsored research, institutional money is often great for single-PI projects.
So I don't think you can draw conclusions about research type -- most folks I have worked with won't touch their non-sponsored funding if they don't have to. Rainy day funds are difficult to acquire, and many save them to the point of retirement (and in fact, beyond). The ability to have non-sponsored funds and charge a postdoc for a new project without having first found sponsored funding
(which probably requires data, a proof of concept, etc.) is a great benefit--whether it's a basic, applied, or development project. Non-sponsored funding is startup money, seed money, bridge money, money due to administrative service that you can then use as administrative mistake money (that's only half a joke)--overall, it's a way to sleep at night for many PIs; it's not generally a strategy to fund a specific idea for a large part of the research for the average portfolio; it's an emergency escape hatch. Any research administrator worth their salt knows to ask you to spend all sponsored funds prior to non-sponsored. You always use restricted funding for any expense that can be directly charged (according to the terms and conditions of the award) before you tap into your flexible and less-restricted funding. Just period of performance alone is a huge hinderance in sponsored research, and the ability to work without such a constraint is a huge benefit.