I'm not sure the alien's weapons are better actually.
From a recent playthrough I tried on the stable version, I noticed my human weapons far outperforming the alien's weapons at every encounter.
Sure, the aliens have more powerful hitting weapons, but I could easily rattle through 3 or 4 aliens that lined up while they rarely hit me, and rarely killed me if they did hit. I was using combat armor, which I start with. The fine alien armors didn't have significantly more protection that my armors either. At best, they start on even footing with humans.
There was never a mission where they killed me more than I killed them, and considering they are supposed to have far superior technology... I would have liked:
1) If it was almost impossible to manage to kill an Armored alien with the starting weapons.
2) To Start to win the war, you'd probably need to kill an unarmoured alien, steal his weapon, and then run back to the dropship to escape with it, so you could research it and perhaps start gaining some tech.
3) It would be nice if the civilians did have extremely weak weapons compared to what you can field. Maybe enough to kill an unarmoured alien with several shots, but they should be able to have a general (weak) handgun or shotgun lying around they can perhaps start shooting with. Perhaps some of them will be panicy and shoot at anything that moves, but alas, if you have combat armor, it probably won't do much to you anyway.
4) With regards to armor, it would be nice if the first armor you start with is good against your own weapons, so if you accidentally hit yourself (or a civilian does), it won't do near the damage an alien weapon would. Right now, if memory serves, your beginning armor can't defend against anything you can field, whereas today, in the current world, (from what I understand of howstuffworks) we have body armors that can withstand anything from machine guns to powerful shotguns easily, if you get hit in an armored spot anyway.
Well, anyway, enough random rambling I guess. I just felt the game started way too easy, and nearer the end, after I got better body armor, I could easily take on every mission without anyone getting killed, which seems really unrealistic if they outnumber me, better detect me, and have superior weapons and armor, which will probably be geared towards defending against my type of weapons if they did any previous scouting... Err, I mean...