Technically it isn't Alpha Centauri that forces you to choose which kind of evil- it is 40K.

They have
-End justifies the means
-Utopian
-Uncaring
-Hungry
-Sadistic
-War loving
-Insane

As for the Advent they got kicked out for rather obvious reasons- they were differant in such a form that was incompatible with Trader society. It wasn't any one thing- it was the cumulative effect of all their deviance which made them unaccpetable. They rejected the basis for Trader society (individualism, social mobility), their culture (privacy, freedom) and their values (family, wealth).

The greatest of the advent's sins was, though, that on first contact, the TEC's attempts at trade didn't work. That was the one truly unforgiveable sin, to them, and what caused their exile.

Anything else could be forgotten by the Trader Worlds, but that defied their purpose; their raison d'eitre, and it had to be expunged. Not only did they forbid contact with the Advent, which had not even attempted to make contact with the TW, they conquered and then exiled them.

Oh yes, their sins are coming back to haunt them. With cleansing brilliance and visions of madness and beauty.

(Or something equally poetic.).

Of course, the Advent would probably be correctly described as deviants, at the least. 'Unrestricted biological experimentation' doesn't sound entirely wholesome.

I agree with the previous poster that the sins of the solar empire refers to the TEC's mistreatment of the advent as well as their slide into apathy due to their single minded pursuit of money. Both of these sins have come back to haunt them, as sins tend to do.

I beleive it also applies to the Advent that have sinned by commiting sins against nature in order to achieve thier advanced mental powers.

It is also the sins of the Vasari that have wacked off what ever is chasing them. Sins so great it has all but destroyed their empire.

Hence this is why "empires" is plural in the name of the game, all three empires are facing the product of their sins.

However sins are not all bad.

Hehe, much like I was going to say.

Both the TEC and the Advent are of human descent, hence the pysiological similarities.
From what I can gather from the Lore section of the manual and the website, the game is set at least 1500 years in the future. Humanity spread out from Earth and colonised nearby star systems, then fragmented and began fighting amongst themselves (only mentionned as the 'great wars' in the Advent history section). The pre-Advent were a small fraction of a faction that settled one planet (looks like an arid desert planet, reminiscent of Dune, in the intro) and were messing around with implants and genetic engineering.
Maybe there were some kind of super-soldiers created during a 'great war' that beget horror stories of the evils of genetic tampering and implant technologies, its not explained, but when the newly created and expanding Trade Order (re-connecting the shards of humanity to a greater whole or so they would have everyone believe) they encountered the pre-Advent and were disgusted and horrified by both their experiments and burgeoning collective consciousness.

Such a society would be dangerous to a purely capitalist society and so the Trade Order banished them (under threat of destruction) to a far off system, so they could get on with their trading.

So 1000 years later, the Vasari have attacked the Trade Order, which formed the TEC to fight them off but left themselves vulnerable. The Advent want some payback, and have become even more powerful in their exile.

Evolutionarily speaking, both the TEC and the Advent are human still, but they might not be technically the same species any more. If they can breed and produce fetile offspring, they are still the same species.
I don't think you'd get many volunteers though, from either side.

This is probably too much information and detail, but hey, I'm bored at work.
Couple of wikipedia articles on the subject of species and evolution, if anyone's interested:
Wikipedia - Species
Wikipedia - Divergent evolution