They are similar words but have slight differences in meaning;
banal: that which is common, predictable, containing nothing new (unoriginal)
trite: worn out, cliché, overused to the point of not being effective (excessively used)
However 'trite' isn't a word that's used too often (I had to look it up!) whereas, ironically, 'banal' tends to be overused by people wanting to sound clever (thereby becoming trite!)