Should I get the re-release on the Xbox Live Arcade, or buckle down with an N64 copy?

Why would you not get the XBLA version? It's also backwards compatible on XBO now.

I don't know anything about it besides the fact that it exists, sorry

There's no reason to hunt down an N64 cartridge when you can buy it on XBL for $15.

I don't know the difference between cartridge and download in terms of quality, but the game is great.  Also the second one is a bit better!  Enjoy it this is one of the titles I always go back to

Depends on you really. If you just want to play the game, then feel free to just get the XBLA re-release. If you want the original experience though, then go for the Nintendo 64 version. While the core game is the same regardless of which version you get, there are some differences between the two. For example, direct references to Nintendo have been removed in the XBLA version, but the scrapped Stop 'n' Swop feature between Banjo-Kazooie and Banjo-Tooie has been re-added in the XBLA version.