Listen, let's look at the facts, shall we?
(Spoilers ahead.)
A gundam is a mobile suit, just hyped up. It can be armed with quite a few weapons, ranging from scythes to beam guns or whatever. They're roughly 17-40 meters in size. Most gundams are able to fly and leave the Earth's orbit. It's power supply is used by reactors, in where no cord is necessary. (Or something along those lines.)
An Evangelion is an angel, just with a mechanical shielding around it. Standard equipment is normally a rifle along with a "Prog knife" (a switchblade, basically. Apparently it can cut through AT fields.) Now, evas are like, 1,000 jillion meters tall. Much, much taller than a gundam. It's leg (probably less) is about the size of a gundam. Evangelions are designed for ground combat only, and they have miny boosters. (In a certain episode when Rei goes down into an elevator shaft or something along those lines, before she hits the bottom, she activates some sort of booster thing that helps lessen the impact.) It's power supply comes from an eletric cord, and when that cord snaps, it runs on a five minute battery. (Or was it 8? 10? I don't remember.)
Now, let's compare their armor.
Gundams: Gundamanium alloy, or something, I don't know.
Evangelions: AT fields. AT fields are literally IMPOSSIBLE to penetrate with artillery, missles, bullets, shells, nuclear bombs, etc. (Maybe an n2 mine, but I'm not sure.) The only thing that can penetrate an AT field is an angel or the lance of loginus.
Obviously, it's impossible for a Gundam to kill an Evangelion. But since I just wanna prove my point, I'm gonna go on.
Let's inspect their controls.
Gundams: Controlled by hand and a bunch of things which is almost impossible to memorize.
Evangelions: Almost all of it is simply mental.
Evangelion pilots simply have to think about what they want their Evas to do, meaning they can do some pretty awesome stunts. They can fight almost like a human, or better, while Gundams have to be controlled much more akwardly and aren't as fluid in motion. Plus, if the pilot freaks out or something, and forgets the controls, gonna be much harder.
Now, to get to my last part.
We'll check out how the actual battle would play out as.
Let's put Eva unit 1 against Deathscythe. Deathscythe rushes up, slashes with scythe, doesn't even faze AT field, Shinji becomes angsty for a moment, then ends up blowing Deathscythe to pieces.
Eva unit 1 versus Heavy Arms. Heavy arms launches huge barrage of missles, doesn't faze AT field, Shinji becomes angsty for a moment, then ends up blowing Heavy Arms to pieces.
It'll just follow that pattern.
Conclusion: Eva pwnz0rz Gundam, no matter how much you say that the gundam boys are prettier, and look cooler. Eva 0wnz that match. (Infact, Eva pretty much owns every match. whee )