'Perhaps' and 'maybe' are both fine in BrE; but I remember reading on another thread that 'perhaps' sounds a little stuffy (or prissy), to American ears.
(Quite often, 'perhaps' is pronounced 'praps' by BrE speakers.)
Perhaps you might say that the 'maybe/perhaps' at the beginning of the sentence puts the emphasis on what follows; whereas at the end of the sentence, it has an air of retrospective doubt – maybe.