A wee bit. With Eddie and Chris, there was a more personal history between them as they made the leap from WCW to WWE together and achieved their peaks within a couple months of each other. They both had problems with injuries that delayed them having a good program together for the first couple of years, but when they were both on SmackDown from 02-ish onwards it reinforced their personal rivalry. Bryan and Punk just haven't had that same exposure.
I realise Bryan and Punk do have a somewhat similar backstory, but because it hasn't been that prominent on TV, it struck me more as "2 ex-indie guys" rather than "2 best friends".