Are there any perceivable in-game consequences of going for either of the two solutions (letting the gang take Bertram, or defending Bertram from the gang)? Do I get to meet Little Red later in the game, if I let her live? Or does Bertram end up in an even bigger mess?
No, the Little Red quest is standalone. You will not end up meeting Little Red later on and doing a different quest or anything.
The only tangible difference between the two options is that one requires you to fight Little Red and her gang versus not having to fight anyone. The former option will net you 50 EXP and 10 Crowns, while choosing the latter will net you 25 EXP and 20 Crowns.