I personally prefer MonsterHunt and here's why:

MonsterHunt in UT99 was a lot more fun. Each map was like an adventure. Each map had it's story. It was like a small scale MMO. Players were racing not only in the form frags, but they also wanted to be the first to reach the end of the map and see themselves standing there, pelvis thrusting, waving at the others. Players were gathering before portals that lead to bossfights, almost as if they are preparing for a raid. It had quests! Often you had to search for keys or switches on the map or portals. Gather most to progress, gather all for a special reward (like instagib). It had a variety of maps with underwater and airborn missions.

In UT2k4 there's nothing in comparison to great maps like Andromeda Ancient, Skylands 1-3, SkyBlueFound 1-2, Long Corridor (2006 version), jikyu800-en, Nali Village, Krall Fortress, WinterHouse, etc. Invasion is a completely underwhelming experience compared to MonsterHunt.

Moreover, MonsterHunt also includes survival on DeathMatch type maps like Invasion.