I wish you could play as the aliens.
Obviously certain changes would have to be, an if this was ever made, it would be a lot of work.
Difficulty levels would be described as Sectiod, Floater, Snakeman, etc. I'm sure I'm not the first one to think of this general idea or this difficulty idea.
Certain gameplay elements would change. The mind probe would reveal the location of every human member of xcom and thier stats.
I would replace money with influence. Basically, you are the alien supreme commander (The Red muton from the intro), and every success grants you greater influence with the brain. You want better ships, and weapons, well you need influence to convince the brain to go along with your plan.
If I was playing as aliens, there are certain gameplay abuses I would commit. I would immediately kill my own navigators, leaders, and the Commander. I would also destroy nav computers and when possible, power sources (plasma pistols can't destroy them). So to curb that, a negative influence system needs to exist. I would call it Desperation, killing any alien or destroying important materials earns you desperation pionts. Once the Humans have caputured thier first navigators/leaders/Commander, then the kill penalty would be lessen. There are only 2 ways to reduce desperation, new influence will gradually reduce it or perform a redemption mission.
A redemption mission is basically a special terror mission/base attack lead personally by you. If you fail in the mission, or you the commander are killed, its game over. Its ultimate goal is to kill or (preferably) capture a human leader of a powerful country (funding country maybe). It would be 3 stages long. The first stage is a terror mission with civilians and xcom if they are close enough. The 2nd stage is an all out battle with 40 human soldiers armed with conventional light and heavy weapons (harder difficulties and later in the game, the soldiers might have lasers and alien alloy armor) The last stage would hold the human leader, a few civilians, and a bunch of special forces well armed (including mines and prox grenades, maybe alien weapons even) and with good stats.
If the humans make an avenger and capture a commander, they might attack your mothership. One of your big command decisions is the location your mothership near earth, or behind the moon, or in geosychrosis orbit above Cydonia. The closer to Earth, the easier it is to make influence and run missions, but if you orbit Mars, you can intercept or are attacked by the avenger. Win that battle, win the game.