To be clear, Tomb Raider: Definitive Edition is the same game you may have played in 2013 on last gen consoles/PC. If you're expecting an expanded story, levels, etc., you'll be disappointed. If you're looking for a better looking version of one of the best games of 2013 with some multiplayer DLC included on-disc, you'll be quite please.
I can't say that the Definitive Edition holds the same "wow" factor that Tomb Raider did on Xbox 360 - the game looked great then and it's not a giant leap over the PC version, but it does look better. The key here is the awesome gameplay has not changed. The shooting and platforming are still fun and the explosive moments still stand out. If you've played Tomb Raider, you can probably wait to try out this version but if you haven't, no excuses. Play one of the best games of 2013 and now 2014.
Anyone who says the PC graphics are better hasn't played both. Just do a quick search to see plenty of examples of how much better this looks on xbone. Not only does it look amazing, gameplay is spot on. Been playing the series since the original PS days and this is as good as any release to date. If you've already played it on another system it's probably not worth another run through, but if you haven't played through this one the xbone or ps4 versions are the way to go.
I have only played this game on the xbox one and thought it was awesome and so much better than I expected. I honestly expected to not like it. Lara is a beautiful looking chick that you don't mind running around with, and I was sad to say goodbye. The graphics helped with that.
Jumping from ledge to ledge and climbing wasn't as difficult and awkward as a previous game I've played in the collection.
I didn't find it difficult to go back for collectibles. And thought that it was cool once you cleared out an area, enemies didn't respawn and the area was yours for collectible hunting.
After playing the Assassin's Creed game on Xbox one, I felt this game had many similarities. If you liked that one you'll probably like this one.
The free roam was pretty good. Climbing and jumping was usually good. Graphics are awesome. Well worth the rental. Not sure about owning it once completing it, it's usually like that with most games though.