Neither pronunciation of piste (with /ɪ/, like pissed, or with /iː/, like pieced) seems to be strictly localized to a specific geographical region (which is not surprising, I think, given that it's a rarely-heard word and it's likely a fair amount of people base their pronunciation on its spelling).
Currently, in both regions it seems the /ɪ/ pronunciation is rare and the /iː/ pronunciation is predominant. The comments by Peter Shor indicate that it's possible the /ɪ/ pronunciation is more common in the context of fencing. However, I only saw one person in this forum thread who mentioned hearing or using this pronunciation, and BladorthinTheGrey left a comment here saying "I live in Britain and I am a fencer, I have never heard anyone pronounce it with an /ɪ/". So it seems even in fencing it is quite a minority pronunciation.
The Oxford English Dictionary records the "long e" pronunciation as current for both British and American English, and it also has a note saying the N.E.D.(1907) gave the pronunciation /pɪst/ for the variant of this word spelled pist.