I'll throw in my 2 cents since I've been HH Diamond for 9 years and PC Platinum also for several years and have used both HH and PC points for hotels in Europe. I would recommend HH Gold overall, since HH status carries more weight in Europe than PC. As a diamond, I was treated like a king at Hiltons in Lyons, Paris, Athens, Stockholm, London. Intercontinental used a separate program from PC until a few years ago - Ambassador, so if you just want cheap digs for less points in Europe, PC points will also work for both HI and HIExpress there. I've stayed in Intercontinentals (Barcelona, Rome), but HH points in Europe - my humble opinion: seems to be more for 5-star type hotels.
As a frame of reference, anyone can pay $50 and get PC Gold status. I talked to a PC staffer who told me there are a lot more PC Platinums than Golds, so it doesn't appear to be an exclusive club.
Also I recently got the Barclay's BA card too. Don't count as an automatic the 100,000 miles as two tickets to Europe. I already have 100,000 BA miles and they don't seem to be worth as much as any American-based carrier's 100,000 miles, although I haven't seriously tried to redeem any yet.
YMMV
-outoftown