To be entirely fair, there isn’t a big difference between these two rule sets at a macro level. Pathfinder was intended as the next step of D&D 3.5, trimming down the rules to remove complications and re-balancing the game’s power so the often under-powered martial classes could stay relevant during higher levels. As a result, it is fairly common to adapt things from one version to the other. For instance, most of my D&D games incorporate the character sheets and skills of Pathfinder, along with a few other rules–such as cantrips (the most basic, lowest-leveled spells) can be cast without limitation and all combat maneuvers are performed using the rules from Pathfinder rather than 3.5.
I find that combat runs a little more smoothly, skill allocation is easier, and general player satisfaction is higher when I incorporate these rules. It allows me to bring in a bit more power to skill-based characters without running into what I believe is the biggest problem of bringing Pathfinder rules and character stuff into 3.5. As a whole, the core components (character classes and racial abilities, mostly) of Pathfinder achieved a state of balance by increasing everything’s power. There are exceptions, of course, but it can be frustrating to try to balance a character built using 3.5 rules with a character built using Pathfinder rules.
3.5 can also be hard to adapt to Pathfinder because it has a similar problem. The core components may be weaker, but 3.5 has a wonderful array of extra feats, class variations, racial features, and poorly balanced errata that make breaking the game much easier. I can build character with limitless power in 3.5 and I’ve yet to find a way to even break the game on the same scale with Pathfinder. I can make a character that can easily move a mile every two minutes (and I know I can get it higher if I try) in 3.5 and that’s just silly. I can create cell towers and rail guns. I can do pretty much anything, if my GM doesn’t know to stop me and I’m feeling perverse. The only thing that redeems 3.5 is that it takes very specific knowledge (which anyone can now find online) to build those things and your average player doesn’t want to break the game.
When it comes down to determining which variation you want to play, 3.5 or Pathfinder, I find it breaks down fairly well. Either works great for role-playing and story-telling, but 3.5 works really well for players who want complex builds or have more experience. Pathfinder is great for people with less experience or if you want to keep your campaign simpler and more focused. I can’t count the number of times I’ve had to remind a player in one of my 3.5 campaigns that, just because he found it in a rule book, doesn’t mean his character knows about it or would even be able to obtain it. This has been happening a lot in my weekly campaign, which can be frustrating at times because he keeps accidentally trying to min-max his character. If we were playing this campaign using Pathfinder, I doubt he’d be able to get up to even a quarter as much crap as he does.
The few times I’ve played Pathfinder, it worked really well for introducing new players. The abilities were much more clear and I didn’t feel like I needed to spend a few days browsing books, PDFs, and forums to figure out how I wanted to build my character. Every time I’ve gone and done a pick-up-and-play campaign at a game store, it has been a Pathfinder campaign. I’m certain the latest edition of D&D (5.0) would be just as easy to pick up and play, but I feel like Pathfinder has more depth to it for the people who want it. You can still get multipliers to your power level instead of just adding to it.
I really want to play more Pathfinder, mostly to learn more about it. I don’t own any of the books and everything I’ve read about it has been what they released online as part of their System Reference Document (search the version you want to learn about and “SRD” and you should wind up with all the rules you need to play). I’d like more experience, both as a player and as a GM. It can be fun to experiment with different rules and see how far you can go, but there’s also strong appeal to playing without all of the crazy extra stuff. Just like when I want to play Skyrim without any mods sometimes, despite loving what the mods do to the game.