I pronounce them the same way.
So do I. But the diphthong /ʊǝ/ is in a state of flux. Most dictionaries say that there are 44 English phonemes; but Longmans - in the interactive IPA alphabet distributed with New Cutting Edge, only give 43. They don't include /ʊǝ/.
For example, some people (many - including me) pronounce 'door' with an /ɔ:/ sound; (I don't usually say 'rhymes with', for reasons I've discussed elsewhere, but for me this is a homophone of 'daw' - the bird, more often met in the compound 'jackdaw'.
{Hmm, is that a male, a female being, properly, 'jilldaw'... NB this isn't a serious speculation.;-)} Someone who does something is a 'doer' (/du:ǝ), and if he doesn't enjoy it he might have a 'dour' face /dʊǝ/.
But I do distinguish 'pore/paw' from 'poor': /pɔ:/ but /pʊǝ/. Many people don't.
I suspect that speakers of extreme RP might use the same vowel distinction for 'morning/mourning'. But if they do, they're in a tiny (and vanishing) minority.
b