Personally, even for simple games I prefer for collision to be handled at a higher level than the individual objects involved. In a simple game, objects might have hard-coded responses to collision (e.g. bullet hits player, remove bullet and call player.hurt()). In larger games, an object can be notified when a collision occurs and can determine its own reaction. Larger games again typically separate physical simulation from game objects entirely by introducing a physics engine.

For smallish games, the actually collision detection might be in the Level object, or even a higher object again such as a "World" object which is aware of both the level and the game entities - it can be nicer to let the Level concentrate on handling tiles and not worrying about the game objects too.

I'm not sure the two approaches you mention specifically make a huge performance difference, other than having a collision logic scattered into a set of different game objects complicates adding broad algorithmic optimisations (e.g. spatial partitioning). However, a third alternative to the approaches mentioned is to avoid storing any state in the Player but instead pass either the level or the Tiles to the update() method as parameters.