No. The polarising effect is the same. Some people claim that linear polarisers have a stronger effect that circular types, but it's not true. After all they're just a linear polariser with a quarter-wave plate on the back. No difference between cheap and expensive types either, at least on polarising ability, if not other important things.
The Hoya HD is noticeably lighter toned than most others, 1.2 stops of overal exposure reduction compared to 1.7-1.9 stops of most others, so if you need to keep shutter speeds up that's an advantage. But it polarises just the same. I've tested loads of these things!