I made a series of calculations, using the OD&D Fighter XP progression as a baseline:
Level 1: 0 XP
Level 2: 2,000 XP
Level 3: 4,000 XP
Level 4: 8,000 XP
Level 5: 16,000 XP
Level 6: 32,000 XP
Level 7: 64,000 XP
Level 8: 120,000 XP
Level 9: 240,000 XP
I did my calculations based on the pace (in terms of number of sessions) needed to level up.
I did this for three scenarios:
1) earning enough XP per session for an unmodified fighter to level up once every 20 sessions
2) earning enough XP per session for an unmodified fighter to level up once every 10 sessions
3) earning enough XP per session for an unmodified fighter to level up once every 5 sessions
I then plugged in the numbers for XP per session for a fighter with no XP bonus, and a fighter with a 10% bonus for each of those three scenarios.
This is what I came up with. The yellow cells are where each fighter (bonus and no bonus) levels up.
As you can see, the fighter with the 10% bonus gets no significant edge over the fighter with no bonus at all.
In a campaign with an extremely slow level progression (averaging 20 sessions per level), the fighter with the 10% bonus starts to pull ahead around session 37 of the campaign – leveling up three sessions before the fighter with no bonus. But of course in this scenario, it's taking 40 (or 37) game sessions to hit level three.
In a campaign where PCs progress at twice that speed (averaging 10 sessions per level), the fighter with the 10% bonus starts to pull ahead at session 19, but only levels up one session sooner than the fighter with no bonus. The fighter with the bonus stays exactly one session ahead for the next 20 sessions and for some time beyond (though the next scenario suggests he will widen the gap a bit more much later on).
In a campaign with relatively rapid level progression (averaging 5 sessions per level), the fighter with the 10% bonus pulls ahead only at session 35, and only by one session, and then only because the XP requirement to progress suddenly stops doubling. If the XP progression kept doubling, it appears the fighter with the 10% bonus would never pull ahead of the fighter with no bonus.
So it seems that unless a) you play with a really slow level progression or b) you get to higher level play where the XP requirements flatten out, a 10% XP bonus will have no appreciable effect on game play.