Some PI's are of the variety that the recruit based upon the specific project they have to get off the ground (i.e. just got funded). Some recruit because they have this idea that they need prelim data on. Some PIs are in the boat that you can do whatever (within reason) that you are interested in. There are pitfalls to all of these.

In the first case, you have a pretty good project that is funded, there's some prelim data on it, there is direction. Downfalls: your PI has a very specific place they want this to go, so while you may have all the footwork done, you if you don't get the exact information that they want, they could give you bullshit 'confirmatory' stuff to do. If your PI is standup, you could probably get out soon. But, you probably are going to have to do an additional post-doc to prove your worth and learn some more techniques.

In the second case, it's kind of what science should be, there's a question, an idea, and someone needs to do the work. This might take long because you might have to develop something/make something. This might be very rewarding though. If it get's funded, great, but you should be aware of the fundability of the project.

The third case (and I will admit that my own PhD experience was more 3 than 2), you learn a lot. You are going to be there a while (unless you have magic hands), but it's a project that you came up with, something that you have invested in. There are also going to be funding hurdles, and there are going to be PI hurdles. PI hurdles include them not remembering what you are doing and why, or not getting it at all.

Sure, these are broad strokes, but picking your project is a broad stroke. You pick it based upon where it's been and where it's anticipated to go. It's like a stock, past performance doesn't guarantee future returns.