I've played all three: A Game of Thrones, Warrior Knights, and Britannia. In fact I own all 3 as well.
To start, the win condition in Britannia is very similar to the other two, conquer territory. The difference is in the reason for warmongering, however. In WK and aGoT, you conquer territory to gain influence, new units, more money, and to win (in both, you must conquer and control cities). In Britannia, you are rewarded for achieving the historical aims of the tribes that you control. This doesn't always mean recreating history exactly. For example, many nations want to control York, but only one can do so when the scoring round arrives. This creates the conflict. Do I try to deny points to my opponents with this tribe? Do I try to score as many points as possible with this tribe? Do I expand as much as possible? Do I commit all of my tokens to break my opponent?
If you've chosen to disrupt an opponent because you think you can get more out of that move, you must then decide which opponent to attack, which of his or her tribes, and when. This involves knowing who is winning at the time. Usually in the beginning, the Yellow player (who controls the Romans) will have a huge lead in points, but that does not mean that he or she is winning. Flinging all of your Welsh troops at Roman forts could allow the Roman player to easily conquer Wales, and rectify slow progress against the Brigantes, for example. This in turn allows the Brigantes to attack the Romans or the Picts, which might allow the Red player to surge ahead. These types of scenarios are what make the game really interesting to me.
For example, in one game I was playing as the Red tribes, and toward the end of the "dark ages", I had made Saxon England, instead of Anglo-Saxon England. This allowed the Danes to march on many territories unchallenged, and it eventually resulted in the Green player winning because I was thinking too short-term to see the big picture.
Another big difference between the games is the lack of resource management in Britannia. The resources are very abstract (specifically, only "population" is tracked along with your victory points), and this allows the player to focus on the overall strategic situation which I find to be a good change of pace in this game. It also allows the turns to flow one you get the hang of the mechanics, which is greatly needed because there are a lot of turns and there is no way to end the game early.
The final point I will say is that even if one of your tribes is eliminated, you always have another invasion to look forward to in a few turns, and you can plan ahead to decide how best to regain a position of power on the island.
This game is a big investment timewise, but I think that it accomplishes what it sets out to do. Don't let the unbalanced positions fool you, the game is very well balanced and any color or player can win. Also, even though combat is die-based, there are enough battles to allow everyone to have a bit of bad luck and a bit of good luck, so I have noticed that there is not a lot of complaining about the dice. Though sixes against Romans do seem to be scarce in the first few rounds...