Glider
Captain
The actual advantage(s) gained were amongst other things a huge advantage in performance. Once airborne nothing the Allies had could touch the Me262 if it was well flown. Problem was however that the lack of fuel trained pilots, as-well as the huge numerical disadvantage the German suffered from, kept them from ever being capable of capitalizing on the actual advantages the Me262 introduced.
As for its performance against fighters, it far from lost out, instead it outshined everything else out there. Several pilots scoring over 5 fighters in the Me262 without being shot down once. Also remember that the far majority of Me262's lost in combat were so by being bounced whilst trying to land or return to base. The escorts ganged up on the Me262's everytime one was spotted, never allowing a fair fight.
I think the difference lies between having a potential advantage and an actual one. On this we are going to have to differ. No one will disagree that the 262 had a huge performance advantage but the circumstances meant that it didn't deliver any strategic advantage.