See Xbox 360 Edition.
The company responsible for the port is 4JStudios, and so I imagine its entirely up to them how much of the functionality that they choose to port and how frequently they choose to update it, however the Wiki does state that "Updates will be free of charge" (which implies that it will at some point be updated free of charge with new Minecraft features).
The "Gameplay" section fairly concisely lists the current gameplay differences, most notably I imagine that some of the intended differences (such as the difference in the crafting system and in the UI) will mean that some features of the PC version of Minecraft obviously won't make much sense in the XBox version.
The Xbox 360 edition is currently based on an earlier version of the
PC edition (Beta 1.6.6), and therefore lacks some items and features,
such as sprinting.
For the most part the Xbox 360 edition of the game is identical to the
PC edition, but has several notable differences and features:
The player can optionally make use of Xbox Kinect functionality to assist in their gameplay, although Kinect
functionality was not available at launch.
The Xbox 360 edition doesn't make use of the standard crafting interface as in the original version, but still has similarities to
the PC's 2x2 and 3x3 crafting grids. The interface doesn't require the
Player to place items in the correct place in a crafting menu, but
simply shows the blocks required to craft the selected item, and
crafts it if the Player has enough blocks.
There are 8 default skin types, all of which appear to have Steve's face, but wearing different outfits.
The game features split-screen functionality, however an HDTV with a Component or HDMI cable required for Split-Screen play. Up to 4
players can play in split screen*, as well as the possibility to play
8-person online multiplayer game modes in split-screen.
Mods, Texture Packs and extra player skins will be available much later.
The Xbox 360 edition includes a tutorial mode not included in the PC version of the game. This tutorial leads the player through the
basics of mining and placing blocks, crafting, as well as building
their first house to survive the night (video).
You cannot change a world's difficulty mid-game. You can change it when you select the world for play.
You always begin a new world with a map.
Unlike the PC version, each world in the Xbox 360 Edition is currently limited to 1024 by 1024 blocks. This is approximately the
size of an in-game map. It is expected, but not known if the world
size will be increased along with the updates that will bring the Xbox
360 version of Minecraft up to date with the PC version.
You can not walk through Sugar Cane.