Sentence 1 means that he demands the best service, but nothing more.
Sentence 2 means he demands the best service and nothing less, thought he may accept more.
So, in sentence two, it is implied he is more fussy, whereas in sentence one, he values service but isn't too fussy about other things. But essentially the meaning of the two is not very different in this particular case.
Usually nothing less is paired with something valuable, while nothing more is paired with something humble. This is to emphasise in the first case that the person is demanding high standards, while the second is minimising the amount the person is asking for, lessening the demand.
I hope that made sense! :)