Even uber powerful Gundams like Wing Zero or the Double X doesn't even stand a chance of defeating Unit-01, they are simply not powerful enough to take down an Eva, especially when it's berserk. A Gundam, if lucky, might be able to harm an Eva, but it would just regenerate anything it loses.

Uh.. You DO know I was kidding right? I was mocking the series my boy... In a Gundam versus Eva fight, I'd go with the Gundams winning the first 3 minutes- giving Shinji his time to freak out and pee in his pants and warm up, then the next 10 minutes or so of the Eva beserking and ripping the pilot out of the Gundam and eating him while Shinji vomits. Gundam pilots may be good along with their also unnaturally strong and irrealistic mech suits, but it seems their weaknesses are their pilots, unlike the Eva that can go without Shinji. Plus Gundams look like theyd snap apart easier, while the Eva's fleshlike body would take longer to yank off. Power-wise, it might not be able to fight long range, but most Gundam fights end really quickly close up, because most of them depend on their huge guns spraying all over the place to destroy their grunt enemies.

Melee Specialist Battle:

Athrun vs Eva- Yeah using Fukada's reused screen caps, Id say the Eva would rip the head off of the Gundam first as Athrun sliced through Eva's arm. Once the sight is out, the Eva will continue its way into the cockit-pit.. Next.

Kira vs Eva- LMAO This dude can't fight up close. Depends on his weaponry too much. Next.

Amuro or Char vs Eva- Funnels.. That may be a problem, but then again running out of ammo against the Eva would be a bigger one. They smply wouldnt be able to destroy it before they ran out of ammo and other crap. Beam sabers would slice through an arm or a leg, but then the second they do that, their gundam would get trashed and eaten.

God Gundam vs Eva- This is a joke right? The AT field. Too slow of an attack that depends on a single thrust that doesnt miss- if it does(and he will against Eva), he's screwed big time.

Wing Zero- Overated piece of garbage will get its wings eaten. Sucks monkey butt at melee fights. Dont tell me those huge-ass wings dont get in the way of a melee fight. Heero's Zero system would be better off with Quatre when he's insane.

Turn A- Another pilot versus rabid animal on the loose problem. Might have Eva on the run for a good 10 minutes, but then things will look bad for the Turn A. AT field vs Moonlight Butterfly thing... Hmm.. There would be a 20 second flash of a white screen without sound then youd have the badly disfigured Eva suddenly emerge and grab the Turn A while the pilot is still panting. Then its over. Probably the best matchup though.

In a fight with machines vs man/living things- machines will lose... Watch Terminator! XD Gundams are too mechanical and depend on weaponry, while the Eva can do all the ripping with its bare hands. Half of them dont move fast enough to turn around and face the Eva if it were to go on all fours and decapitate them from below. Actually thatd be interesting since we have yet to see a Gundam face anything challenging from the ground... kick it? I dont think so...

EDIT: Is the Eva invincible? Oh hell no- The Turn A and its pilot might have lost and torn apart, but Shinji is definitly long dead after the MB, and the emanciated Eva will crawl around for a good 20 minutes and die afterwards. A draw then for those two ^^

In my opinion, both of them are the strongest of their seres.
Goku servival from heart disease, and many fearful fight. In the other hand, EVA-01 is more like god.
I just remember that God (I forget the name, but he show up in battle of B(I don't remember either but his forehead have "W" ) fear about Sian (who becoming Yellow Hair).
They are undefeatable.

But there are exception: Have you watched or read "Deathnote" If someone write the name in that, nobody servive.