(not) in the same league as - correct
(not) in the same league with - wrong (or at least unusual)

(from a BE perspective)

Thank you for your help, amw! :)

I just looked it up in the Cambridge Dictionary of American Idioms by Paul Heacock (2003) and I would like to know if native American English speakers would use it. (It does seem to be rather unusal.)

Google hits
*in the same league AS... -> 9,370,000 results
*in the same league WITH... -> 750,000 results

I don't think there's any AE/BE difference. The reason is that 'the same as' is a fixed phrase for comparisons.

Of course you can also be in a league with someone, but that's normally in the literal sense: My daughter is in a soccer league with a lot of kids from another school.

Thank you, hm! Guess from now on I'll just use "in the same league as" - just to be on the safe side.

Thanks again! :)