The first costume, worn by the character in the woods, is made up of a stripy jumper, a Duffle coat, jeans and Converse.
This was to try make the character look as 'normal' as possible... Apparently, Duffle coats are also associated with Britishness - which may give a hint the film would be set in Britain, if it were real? Duffle coats are also quite big and protective from most elements, which implies the character is vulnerable - like Paddington Bear (who also wore a Duffle coat), so also the character could come across as quite endearing.
The second costume, worn by the alter ego, is a black and white suit.
This was intended to imply a sense of authority - smart attire assumes a position of power, and someone with knowledge. Similarly, it adds a sense of suaveness and smoothtalk with insincerity - the personality of the alter ego. Sort of supposedly quite friendly looking, but at the same time authoritative and sneaky - ready to betray his other self.