Evangelions have no use for propulsion systems. For transport, they can be brought aboard aircraft carriers (like in Episode 8, Asuka Strikes!) across the ocean, or in giant-sized ramjets across the skies (as in Episode 18, with Tohji's black Eva, and also in the movie). Actually, it's not even until the first Eva movie that they go anywhere near the upper stratosphere-- and even then Eva 01 does this through the use of some kind of "energy wings." So this doesn't count.
(On a completely unrelated side note, there's reportedly an 'Episode X' out there-- an episode that was cut from the normal 26-episode run. In it, I saw a scene where the Eva is hovering through Tokyo-3 with these energy wings. It was a commercial from my fansubs. No one I know, not even my friend at Gainax, knows what this is, and some of them are actually thinking I hallucinated it all. When I finally did find a tape entitled 'Episode X' I eagerly brought it home only to discover it was an anime porn that was done VERY badly... I suspect it was made entirely with MS Paint! V_V*)
As for Gundams, the earliest mobile suits were propelled by chemical rocket engines until it was realized that super heating the heat generated from the fusion reactor could be used to generate thrust. It was more fuel efficient, and is referred to as a thermonuclear engine. A later development of this, the thermonuclear pulse engine, ignites fuel pellets of helium-3 and deuterium, but is only useful for long journeys in the solar system. This is despite its amazing fuel efficiency. Smaller thrusters are studded across the mobile suit, called Attitude Control Verniers, or Apogee motors. These are strictly for maneuvering, turning, and minor course adjustments.
POINT: GUNDAM (for having an internal propulsion system)
POINT: GUNDAM (for being able to get into space at all!)
*****
Both Evangelions and Gundams are sealed air-tight-- they leak neither water in when underwater, nor leak air out. There'd be a serious problem for interplanetary Gundams if they did leak air!)
POINT: EVANGELION and GUNDAM (for all-terrain access)
*****
"Some people complain about my lack of melee weapons. However, I never intended for you to get close to me in the first place." --Trowa Barton.
Not counting extravagant weapons, both Gundams and Evangelions have a vast array of convention armament weapons. Extravagant weapons include but are not limited to plasma weapons, beam/particle weapons, nuclear weapons, baroque weapons, etc. Baroque weapons are science fiction-fantasy weapons which might include lightning, wind, vibro-, and flame cannons.
Machine guns are seldom adequate to even scratch the Gundam's armor, much less penetrate an Eva's AT field. If you're lucky you may hope for a hit on the main camera, but pilots shouldn't expect too much from them.
Both Gundams and Evas have bazookas (although at the Eva's sacle, they're more like ICBMs-- intercontinental ballistic missiles-- and can be held one in each hand!) and machine guns. They can also carry all manners of rockets and missile launchers.
Gundams especially carry a variety of bladed weapons, from Trowa's pathetic elbow-mounted knife, to the Zaku's hatchet-style heat hawk, and the heat saber used by the MS-07B Gauf and the MS-09 Dom. The crossbone vanguard also had that wacky shot lancer, a hydraulic spear which may also be fitted with built-in machine guns (can anyone say "gunblade"?)
Highly-ballistic Gundams, like the Heavy Arms, have the unfortunate tendency of being weighed down (drastically reducing all areas of speed, acceleration, and agility), and are so limited for additional weapons that they can't carry anything besides ammunition! Once out of munitions, they're little better than the next weaponless mecha. The same is even more true with the Heavy Arms-Custom, which specializes in missiles.
Evangelions are equipped with shoulder-mounted spike missiles (see the Eva movie), progressive knives (they can cleave a jet fighter plane neatly!), handguns (with silencer), submachine guns, swords (Eva 01 and 02 were both originally supposed to be equipped with prog-katanas), uzis, double tonfas (in the unseen Eva 04 production model-- which also had a riot-style shield), long range automatic assault rifles, and a sniper gun (although it had the distinct drawback of monopolizing all of Japan's energy, fire only once before overheating, and being left wide open between its long cooling periods). Due to the sheer size of its projectile weapons, it's assumed that they have larger shells and have better range, but this is only supposition and hence should be disregarded. They also had axes, grenades, and the mother of all melee weapons, the Longinus lance!
The lance is the only thing besides an Angel that was able to easily pass the Eva's AT Field. They're roughly as long as an Eva is tall (14.5 stories-- see entry #3) in both forms, and if you count the original lance with the mass-produced lances, number nine in total.
POINT: EVANGELION (for the nine Longinus lances-- if it were not for this, since I don't know too much about Gundam's conventional weapons, I would call it a near draw, but still in Evangelion's favor)