Strong

1. The Romans (collectively) - The AI fares the best as the Brutii, in my games. The Scipii tend to do worst though they still manage to capture some territories.
2. Egypt - strongest single faction in the game
3. Pontus - They start out weak but always manage to expand. My first game, they controlled most of modern-day Turkey and a few other provinces east. In my second, I was Parthia and near them and we were allied, so they weren't able to expand that much. That said, they managed to grab Nicomedia and Byzantium and were expanding into Thrace when I attacked them.

Weak

1. Seleucids - In my first game, I also experienced Pontus creaming them.
2. Carthage - With how they are depicted in RTW, it's hard to imagine them giving the Romans any trouble at all.
3. Macedon - Dead immediately in my 2 imperial campaigns. Both were purely just the AI, I didn't help their demise at all.

The barbarian factions in the west in my games seem to be quite stalemated. The Gauls tend to do worse because they are sandwiched and have the Julii as a neighbor.