I don't know about the structure of PARC, but I suspect it's not quite as comparable to Bell Labs as you make it sound.
Weren't both of them funding some of their research projects via direct government (DARPA, etc) grants?
AT&T was a government monopoly. They had no meaningful competition that required rapidly innovating AT&T's core products, and they had lots of profit due to their monopoly status. They could afford to dump money into research (in addition to whatever gov't research grants they were getting) and still have plenty of profit left over. That's not quite government funding of research, but many economists will say that given its monopoly status, what it did was de facto government action.
PARC did some great things but they didn't have as broad a range of research as Bell Labs, did they? Xerox never had a monopoly like AT&T did, although I'm fairly sure they got plenty of government research grants.
There were also a lot of open fields in hardware and software that were just starting to be explored back then. Tech companies were investing plenty of brainpower and money into R&D, given little pushes by government grant availability. I think the difference in AT&T's case was the breadth of research due to how much profit they had... again, due to monopoly status.