What is the perceived brand difference between Strategy& and PwC Strategy?

S& > PwC Strategy

Strategy& is Tier2, the company had a chance to nearly match MBB a while ago.

PwC Strategy... is an offshoot of a big-4 consultants.

The below is an oversimplification, but still generally true in my view: the top consultancies are expensive because they rely on people expertise, and typically don't come to a problem with a turn-key solution; they also do a lot of strat work. other large consultancies (tier-2 and below) are cheaper in large part because they have ready-made solutions that consultants just implement; the consultants here are a lot more replaceable.

Yes, MBB is moving down stream; yes, tier-2 and below are moving upstream. Still, their DNA isn't changing much. Strategy& is more built like the former; PwC Strategy is more built like the latter. You might do the same work in either company, or you might not - but if I had to hire someone from either company to do high level thinking stuff, I'd pick the Strategy& consultant everytime.