Something like a third of medical research funding comes from government sources. It is the most transparent and easily quantified source, so it is the one most often discussed. The incentives put upon researchers competing for these funds steer them towards largely mundane, low-risk, low-reward work, and greatly favor large institutions over smaller research groups. This is a proven way to edge out the sort of research that tends to occasionally produce meaningful or even spectacular results, in favor of research that is essentially make-work or pointless in comparison to what could be done. It's why you shouldn't expect much from massive public spending on research: the yield of meaningful work is very low.
The private funding world is mostly for-profit research, and that has its own issues that are driven by the enormous imposed costs of regulation and short time horizons. So as a general rule near all of the really interesting and potentially game-changing research programs in aging and the broader life sciences were started by and are still largely funded by philanthropists. Consider the SENS Research Foundation, for example, or the Glenn Laboratories, or the points made by Peter Thiel's radical philanthropy initiative: too much funding is biased towards the incremental and the meaningless, while ignoring the tremendous possibilities of the near future. So progress is far slower than it might be.
Here are a few comments on the public funding environment from a discussion on the Gerontology Research Group list:
One of the main reasons for a lack of serious anti-aging basic science [is] the current and recent funding climate of academia. As a scientist currently in the middle of the funding rat race, I can tell you why not a lot of scientists want to work on aging. The NIH/NIA/NCI want preliminary data. They want it on every single grant application. If you don't have it, they won't fund it, and this is a relatively new phenomenon (and the definition of "preliminary data" has become significantly more burdensome). Effectively, in order to get new work funded, it has to be partially (or in some cases nearly entirely) complete, meaning that you have to have some other funding source and a functional laboratory *before you get the grant*.
This shifts risk from the funding agency to the investigator, such that if you are using your current funding, left over from some already completed grant or tangentially related to a grant in progress on a new project, you want to be sure that the new project will work, because if it doesn't, you're out of funding and have exhausted the most precious resource you have in securing new funding - your old funding! You won't do things that are hard or risky unless you're a very rich lab (which tend to be entrenched in certain fields that aren't hard or risky, because that's how they got to be a rich lab), because hard and risky things can fail, and then your career is over. Aging research is hard and risky.
There's too much focus on low hanging fruits because of the pressure to publish and get grants. My lab is no exception on this, but the fact is that all my high-risk, high-reward grant applications have been rejected (my more conservative grants also often get rejected, but at least sometimes they are funded). Some years ago I asked a well-known biogerontologist why his lab was doing a certain series of experiments that, while getting results and papers, seemed to beat around the bush of understanding aging. His answer was: "Because I've got a mortgage to pay."