I think the Iconians have gone from weakest (in DA) to being one of the strongest races (in TA). I mean, organic hull plating is awesome, buildings that give +50% planetary economy? Awesome. Self-healing hulls? Absolutely, totally, unstoppably awesome. I had one loser game as the Iconians in which the Dread Lords, due to some passivity on my part, conquered all but two planets in a small galaxy. Those two planets belonged to me, and were defended by uber starships (like 200 beam defense and attack, 1000 hp each after they leveled about 20 times, and self-healing hulls). The Dread Lords sent wave upon wave upon wave of fighters with 100-300 beam attack, would do about 50-100 damage, then the hull would heal most of that before the next one attacked. I clicked Turn over and over for about 2 years, just to see if they would ever finish me off. They never could, and I couldn't take them out due to a totally hopeless economy (two planets to support two ships at 250 bc/week, read: -100000 bc and falling). I couldn't win an influence victory, because silly me, I turned it off. Military would require the Dread Lords to die. I suppose I might have won a Diplomatic victory eventually, if the Dread Lords decided to randomly make peace, as they occasionally do. None of the other races would have lasted ten turns in that situation. Plus, the Iconians start with a +20 morale bonus, and buildings that give +25% morale each, and farms. That allows them to have a great starting economy, then research their merchant complexes and your economy is amazing.
Anyway, that was a bit off-topic. I personally believe that the Krynn are the weakest when the AI plays (for some reason, it thinks that a huge ship with huge defense and only 1 beam attack constitutes a strong military). For me, the Torians are the weakest. I mean, +10 morale and population growth aren't exactly awesome race bonuses. Maybe it's just how I play, but I always get crushed whenever I use them.