First of all, if you send a dropship to a mission and your soldiers finish it, they don't have to come back to base between missions. If your ship has enough fuel and your crew is healthy enough, you can directly send them to another site nearby. All your ammo is restocked too, so you don't have to be skimpy on shots.This has some advantages as you can go to an area and clean up everything and head back to base when you're done. I'd recommend you have an interceptor (or two) nearby just in case the aliens retaliate and try to shoot down your dropship en route.

Secondly, ships seem to refuel/reload a lot faster than in UFO:EU. (Or maybe they don't and the time goes by quicker in Xeno)? I especially notice this with dropships as you can be out and about almost immediately after returning to base. Even with interceptors, they don't need to be at 100% fuel to send them out (weapon reloading is the limiting factor here).
Smoke Grenades. I mean what's the deal with it in Xeno? Smoke doesn't spread much, doesn't last long and some aliens see right through it. Is it worthwhile, because I haven't found a use for them yet. Stun Grenades and flashbangs on the other hand are a lot more useful.

Tanks/vehicles seem to have more armor than in EU. I started to use them as bait which seems to work a lot of the time. Run them over to an alien to get their attention, then slowly creep back to lure them in. Where you lure the aliens to is dependent on where your soldiers are and the terrain. If you're in tight quarters, then lead the aliens back to your shield/assault (shotgun) or heavy weapons folks to shoot. If there is an open area, set some snipers up around the perimeter and take out the aliens from distance. As in X-COM try not to kill aliens with the tank. There have been instances where the aliens follow my tank and shoot at it from the rear and they either miss or hit and do little to no damage.
Countries get a lot more pi$$ed off at you for ignoring their section of the globe now. Gone are the days of getting enough points locally to impress countries globally. When you start out every country will cut funding except for (hopefully) the country your first base is in. Expect that to be a given. I guess the only way to circumvent this is to build bases ASAP to get as much radar coverage as you can.
So there's a few differences. These are the just the ones that pop out at me from recent memory.

- Zombie