I'd say the thing that makes Pidgin more attractive is the fact it's free, whereas Beeper is $10/mo (unless you host the entire stack yourself, and at that point you can't use the Beeper app). Granted, Beeper has mobile apps going for it.

Pidgin is basically dead. When all the big messengers closed off their protocols, keeping compatibility became very labor intensive. It doesn't look like any FOSS has been able to do it, so I'm optimistic about Beeper.

They are two different classes of applications. Beeper uses transports (or 'bridges'), Pidgin is a multiprotocol client.