The only real way to test them would be to use them both in campaigns.
True. And those weren't matchup ideas for arena. Those were matchup ideas for numerical analysis. Arena matches are decided by initiative rolls. You only get a small amount of data from them.
Anyway, my theory is: "for any type of Fighter you make, I can make a Psychic Warrior that is better at doing the same thing."
At 20th level this is true, but it isn't always true before then. Some examples:
One thing I have noticed is that due to BAB there are some tricks a Fighter can do earlier than Psychic Warrior(Leap Attack+Shock Trooper at 6th for Fighter and 8th for PsyWar).
A two level gap isn't much credit to the Fighter though, since once the PsyWar gains the ability he has Psionic Lion's Charge to back it up and does it better.
The same is true for Robilar's Gambit builds, but the difference there is huge. Fighter's have Robilar's Gambit at 12, where PWs have to wait until 17(since they don't get a feat at 16th).
A five level gap is very significant, so the PsyWar actually loses that one unless he starts near 20th level.
Still, there are very few feats that require more than 6 BAB that define a fighting style, so for most fighting styles, the PsyWar will be the victor: even if it takes him 2 extra levels to do it, when he can do it, he does it better. I'm not going to mention the things a PW can do that a Fighter can't, since Ubernoob is very much on top of that.