It's my understanding that the more level you have in any class that can cast turn undead will give better result as you take more levels. Having a higher charisma will also help as both are taken into account. Once you hit a point where you class level and the charisma bonus places you above twice the dc (class level) of the foe your facing, it's bye bye undead instead of them just running away.
Now something that me and Clarissa used to find a bit odd, was that Lex'or my cleric undead slayer, was able to actually better destroy the undeads with turn undead with a lower charisma and lower overall level than her paladin and that was even before he was an undead slayer and before he had the sun domain.. Not sure what to make of this.
The only difference between the undead slayer and the other classes that can turn undead is the fact that undead slayers automatically receives the sun domain which gives an additional 1d6 toward the DC of the undead. Meaning that the undead slayer can potentially kill on the spot an undead that has a DC up to 6 level higher than what a cleric or paladin would be able to do if they did not have the sun domain.
So yes in essence with the undead slayer class, you will be able to turn undead more effectively, up to a point, since there is only 10 levels of undead slayer. So all in all a cleric or a paladin that were 10.. 12.. 15 levels higher than your undead slayer, would still have better odds at turning the undead.