As nouns the difference between praise and adulation
is that praise is commendation; favourable representation in words while adulation is flattery; fulsome praise.
Does adulation mean admiration?
Adulation is uncritical admiration and praise of someone or something.
Is adulation a positive word?
In my opinion, "adulation" does carry a slight feeling of excessive admiration and praise, as you said. ... So in your example, "the band was basking in the adulation of fans," it sounds quite natural.
