MTW
MTW is a big improvement on STW and is just a couple of fixable problems away from being a huge improvement and a great game.
The biggest problem has already been noted in this thread: there just gets to be too damned many spies, assassins, bishops, inquisitors, emissaries, etc., which are counters that clog up the game map. If a small province like Navarre winds up on the border between two important nations--which is not at all improbable--there will be so many unit counters crammed into the province that it will be virtually impossible to find the one you want. The "solution" is that you can use your mouse wheel to zoom in on the province until a small part of the province covers the entire screen, but even so it is sometimes hard to pick out the one you want, and all I can say is that is basically a laughable solution to a problem that doesn't exist.
If MTW could take the entire "special agent" system and reduce it to spreadsheet-style places where players can allocate funds and choose special actions the game would be 100% improved. As is, by the time you get to the latter stages of a campaign the map gets so crowded with soecuak units and micromanaging them all gets to be so tedious that the game virtually becomes unplayable. Basically, the game encourages you to constantly purchase strategic units throughout the game--and the AI does this as well. There get to be literally hundreds of them on the map.
That said, it is undeniable that the strategy game in MTW is GREATLY improved over the strategy game in STW, which was indeed more than a little bit reminiscent of Risk, IMHO. Building the type of economy that can support tech upgrades and the building and support of a huge high-level army requires a lot of thought and attention, good building choices and careful attention to which leader is assigned which province and which office. Diplomacy is certainly not up there with EU-style diplomacy, but it is much more significant than was diplomacy in STW. The strategic AI also leaves something to be desired--once you are at war, it is virtually impossible to get a peace, and the AI will attack you sometimes with suicidal odds.
The tactical battles are still the meat and potatoes of MTW. If you hated the tactical battles in Shogun, don't buy MTW because they are basically the same. The AI is spiffed up a little but not a lot, but the most significant change is that there are probably 10 times as many troop types as there were in Shogun, and there is a lot of replayability in experimenting with different factions and different troop types.
If you HAVEN'T played Shogun, then I will just say that the tactical battles are excellent, the 2nd-best tactical combat simulation of any computer game (Combat Mission is the best). It is true that things happen way way too fast, but you can give orders while paused, so as long as you are willing to hit pause frequently, you can pretty much maintain full control over the battle. (In fact, for realism purposes, you pretty much have TOO MUCH full control, since you can instantly change the orders of any unit on the battlefield. I saw the phrase "telepathic generals" used earlier in this thread, which accurately describes the only way you could get that kind of control in reality. However, I must say I would rather have too much control than not enough. The game system certainly allows the player to create elegant tactical victories.)
An interesting sidenote on my personal experience: I played a fair bit of EU, but I always played either as England in the Grand Campaign or as Iroquois in Fantasia. I think that was at least partially because, although I think I know more about medieval history than most Americans, I found all these "Mainz joines Wuertemburg and Muenster in their war against Aragon" messages to be incomprehensible and confusing. MTW has much larger provinces and only about 1/3-1/2 as many provinces as EU, so it was a good learning aid in starting to get a grasp on the geography of medieval Europe.
I originally gave up on EU, not because I was tired of it, but because other games came along and I didn't feel totally comfortable about plunging into the mess of Continental politics and war. I bought EU II but never played it! However, MTW made me want to play some EU II and I have been having a lot of fun with it the last week and a half. I definitely miss the great tactical battles from MTW, but EU II is certainly a superior strategy simulator when compared to the strategy portion of MTW.
I AM into warfare and combat, though, so I am not really satisfied by EU combat. I think a full tactical simulation a la MTW would be a bit too much for a game of EU II's scope--hell, it may be too much for MTW--but I would like to see something in between that at least allowed the player to choose battle tactics and level of force commitment (i.e., probe to desparate assault). I would also like to see some differentiation between melee units and ranged-combat units, with a combat resolution process that took that into account. (What comes to mind is Conquest of the New World-type combat resolution, which I do not remember in detail but I do remember allowed you to set up your troops in a front rank and second rank.)