Wow, surprising amount of focus on the campaign. Especially since, in every game in the series, the campaign was an afterthought designed to give context to the battles rather than be the main feature.
That said, the campaign is hundreds of times better than the RTW one. The RTW one was sluggish and dull. Even on VH/VH, there was no serious challenge with the Romans. A couple of well maneuvered Hastati would slaughter Greeks, and once you had Greece you were set for the rest of the game. Additionally, you almost never fought battles. You just took five or six armies, beseiged a bunch of cities that had armies multiple the size of yours, and starved them to death. No work at all. Additionally, it became obvious slugging matches between bigger powers, while smaller powers were invariably steamrolled.
By comparison, the BI campaign is very dynamic. There are only a few actual knowns going into it. You know that the Huns and Vandals are going to cut a swath across Europe. You know that WRE starts out huge and will dwindle in power, which can be easily taken if you strike quickly. However, even if you build up a decent empire in Gaul or the Balkans, a big rebellion or a roaming horde can set you back, and you have to be constantly aware of this sort of thing. And Themi: you like building up from nothing, so why not play as Sax/Franks/Lomb/Celt/Alem/Burg/Sarms/Berbs? Especially if you don't horde, it's pretty tough.
Now, on to the more important factor: the battle engine. You don't notice the battle engine if you play the campaign as much, but for those of us in the MP crowd, the BI one is quite possibly the best. Especially since vanilla was arguably the worst. In RTW, one would take the 'best' units, as many as possible, and stack them. A successful MP army will resemble, more-or-less, the armies of the day. Plenty of cheap fodder and backbone units with some elite forces.
Additionally, there aren't nearly as bad of imbalances in BI. Perhaps you campaigners didn't notice it, but to us in the MP crowd, Desert Cav, Urbans, and their ilk made 90% of the units in the game obsolete. Playing as anybody other than Rome, Scythia, Greece, or Egypt was a good way to lose a battle regardless of what you actually did. Now, the closest thing to a loser faction is the WRE(ERE just seems better) and the Berbers, and I have seen effective Berbers(the return of the Hillmen notwithstanding). Additionally, no longer is a faction defined by a single unit. You knew when you saw a Roman being chosen that all you were going to see were urbans and a big chunk of Praetorian Cavalry. Scythians weren't really the nation of Scythia, they were a bunch of Head Hunting Maidens. And so on. Balance blew donkey balls. It's much, much better now.
Now, on to criticism. Historical is the big one, and there are some problems. Notably the Orthodox priests. Catholic priests, yes, they existed. The Orthodox church wasn't even conceived of. I know that Sarmatian women fought, they found archealogical evidence of that. Despite that, the importance and justification for the Virgin units is kind of...specious. The Romano British army is about 90% speculative, but I feel like they did an alright job. The Carriage Balistae MIGHT have existed, but we don't know that. When compared with things like Praetorian Cavalry, I feel I can overlook everything but the damn Orthodox priests.
They didn't bring back the Eras from Medieval, which I feel added alot to the game. It made balancing substantially more complicated but added some more depth to the MP army buiding. They also didn't bring back the Medieval torches, which were just fun.
Overall, I'd say this was a HUGE leap over RTW, a significant level ahead of both Shoguns, and better than regular Medieval. Better than VI? Not so sure. I've been having more fun with it than I did with VI, to be honest, but the campaign isn't nearly as complicated and fun. So I'd put it on equal footing with VI.