Pulling off headshots with your bow and countering melee enemies is amazingly satisfying, and I quite enjoyed scouring the larger wilderness areas for hidden items and tombs - scaling ledges to get hidden caches and using new equipment to open previously blocked areas (though most of these are in the same maps as you find them)
Same here, I've gathered all the collectibles just to see the whole map and secrets. I maxed everything at the end and had some points left I think. Those samurai ghosts were dropping like flies and I was using only my bow for most of the time.
The most tiresome was navigating throught the wrecks near the sea and finding the mines and letters. Tombs were too easy, and it was a sloppy nod to the roots of the series. Very good port, even on my prehistoric rig it worked for the most time like a charm. Not with all the high settings, but whatever, it looked good enough. The game felt like a weird mix of Rambo and The Descent (probably due to the dark palette and all these dark places that we visit, plus gruesome death animations of Lara).
PS. Lara has the best booty in the Underworld part. That swimsuit !