This thread is pretty old but since I recently finished viewing nge I thought I would post my opinion.
It would seem that after reading through the pages the main argument for why an eva would win is because its at field is unable to be pierced by big o. This is quite true. Having said that though it doesn't mean that big o is the immediate loser. He is more like an underdog. If we break it into categories:
Strength: Although both the evas and big o are strong I believe big o is stronger in melee and in ranged combat. however strength won't do much if it is unable to hit the target.
Dexterity: This definitely goes to the evas. No way big o could out maneuver an eva. Thus even without an at field if an eva only evaded and attacked very sparingly it would be hard for big o to hit it.
Constitution: They both seem to be able to take the same amount of physical damage before breaking in essence they are equal.
So far things are definitely looking better for an eva. But then again battles aren't base only on the mech. Its based on the pilot. This is where big o takes the upper hand since roger is much better in terms of charisma intelligence and wisdom. So where does that leave us then? the at field. no matter how great roger is he won't be able to break through it with big o. At least by reading this thread thats what you would think. Even though big o is the underdog he is still powerful enough to do a multitude of damage to the surrounding area.
When you take into consideration that an eva is so much more dexterous than big o the first thing to do in combat would be to damage the surroundings and the grounding thus lowering dexterity (even though this will also lower big o's dexterity). So now lets say that an eva and big o are basically stuck in an arena and the only attacks are melee attacks. Well the eva will still have its at field. Melee attacks are useless. However during the course of nge how many times did an eva or an angel attack directly out of the at shield? For example if an eva sticks out its arm to attack where is the at field in respect to the arm? if the arm extends out of the at shield its pretty simple to see where im going with this. if the at field extends with the arm then there is another problem for big o and roger to worry about since melee won't work either.
If the at field does not extend the length of the arm--->
its not improbable for big o to break off one of the arms and, since theoretically the arm should still be somewhat alive, attack the eva with it using the arms own at field to disrupt the eva's shield long enough for one of big o's multitude of attacks. If the attacks go through I would say there not be enough time for a counter attack and the eva and pilot are demolished in one sweep and the battle goes to roger. However if you don't agree please continue reading below.
If the at field extends the length of the arm--->
So since there is no way to dodge then roger loses this round and must back out of the messed up landscape and consider new tactics. if he can make it out in time.
If roger cannot make it out of melee reach in time--->
Eva and shinji win battle
If roger can make it out of melee reach in time--->
Im sure one main tactic in any battle is to attack the weakness of your opponent. In this case the eva's only weakness is its pilot (yes I know about that other stuff but for now lets just assume for the purpose of this battle shinji is the only one who can pilot eva 01). Since roger is a negotiator its not out of the realm of thought that he can persuade shinji to give up the fight and export the cockpit. Now im sure most of you are thinking "so what?" if shinji gives up then the eva still has the berserk mode. However, this bersek mode doesn't seem to activate unless impending danger is nearby. If shinji or more importantly the eva is not in harms way why would this mode be activated?
If Roger is able to get shinji to give up the fight--->
Assuming that a "win" is not only constituted by the destruction of your opponent without a pilot the battle goes to roger and big o.
If Roger is unable to get shinji to give up and exit from the eva--->
Lets suppose since big o and the eva were already fighting that shinji refuses to negotiate and give up. From now on instead of dodging shinji takes the offensive (since he is resolved on fighting then he will take the offensive). There isn't any way for big o to dodge the attacks in this environment nor is there a way to run since an eva is faster. Roger's best bet is a distraction technique in which you fire one way to draw attention and move another way. At least with this technique he will be able to move to a different environment.
If Roger is unable to psyche shinji out and maneuver away--->
The eva will win.
If Roger is able to psyche shinji out and maneuver away--->
The battle continues with a new environment: Eva has the upper hand and big o is the underdog.
Of course these are just theoretic scenarios but as you can see the battle could go either way even if big o is an underdog. More importantly is the way the mechs are used, how close the pilot pays attention to detail, and how closely the pilot pays attention to his surroundings.
On a final note I would like to think that an at field is not un-destroyable. If it is an extension of the soul then an extremely long battle (supposing big o could survive for so long) would theoretically weaken it since you would think that after a certain period of prolonged anger and fighting a soul would get weakened (unless its an evil soul then I suppose the shield would get stronger

.)
Also if roger wanted to win quickly all he would have to do is cut the power and present no danger. If roger cuts the power then backs away and stays defensive with no counter attacking I don't see why an eva would continue the fight even if it didn't need a power source. If there were no will to fight then why would the eva waste time? since big o can still function after five minutes then roger and big o would win.