Partly due to the sheer amount of content compared to Tri, Unite progresses much better through it - giving you better rewards and requiring what feels like less grinding. Far, FAR better music and monsters too (narugakaruga, tigrex, yian garuga, and kushala daora are amazing), IMO, with the exception of that fucker Plesioth.
The distribution of sharpness is much smoother in Unite.
Longswords, IMO, are handled better in Unite than in Tri - the infinite spirit gauge/easier combo management in Tri makes for kind of oversimplified longsword usage. I think they may have done it in part to compensate for the lack of dual swords (similar to how the sns feels much more combo-heavy in Tri). In Unite, having to alternate back and forth to keep your spirit gauge up and decide whether you wanted it full for additional power and cutting force or using it for extended combos made it feel like longswords had more depth.
Tri has easier internet play unless you own a PS3, at which point it adhoc party makes things pretty easy. Don't bother with Wii speak if you get Tri - their implementation is absolute garbage.
Unite probably starts a good bit slower than Tri, if I remember correctly.