Viking Invasion was a very sound campaign. Lots of factions, lots of variety and an interesting side-line to the core game. As a patch to the vanilla game, it may have been the best of all three expansions.

Barbarian Invasion was virtually a RTW2. Epic and interesting campaign. Something about playing the WRE in that period just catches my imagination. I particularly liked the way it rebalanced the combat, so that defense stats rose (slowing combat), missiles were less uber and even cavalry was a little more fragile. Very promising for MTW2.

Mongol Invasion was an interesting patch. Introducing different start dates to the vanilla game was good, as was changing build times to make things move faster. Only blot there was that it seemed to get rid of some of the chrome - especially Burk Kwok's great voice work on the harvests. (If anyone can tell me how to get it back, I'd be grateful). I never played the campaign. I was not too interested in rampaging around as the Mongols. The Japanese side might have been fun, but when I heard you could win it by defending the first bridge province, I never gathered the enthusiasm to play it. I much prefer campaigns where there's a lot of building and freedom, rather than a slugfest (which is also why I prefer MTW and RTW's core campaigns to that STW).

So I vote MI, although I still bought it (twice ).