I find both ‘What?’ and ‘Pardon?’ rude. The former can come across as abrupt, and the latter has overtones of taking umbrage, as in ‘I beg your pardon - I can’t believe you said that?!’ So both are rude, I think, especially as hearing people tend not to say either with an enquiring expression, which softens both. Deaf people will always use that enquiring expression to seek clarification, and it just seems more polite and less ambiguous generally.
I have different strategies in different circumstances. As a deaf person, I usually say ‘What was that again?’, ‘I didn’t catch that?’ or repeat up to the point I got lost, eg the last term in a list, or ‘Johnny went to where on holiday?’ so the person (a) knows the thing I had difficulty with, and (b) doesn’t have to repeat the whole shebang again, just from that point onwards, and it keeps the conversation flowing.
I might say say ‘Sorry?’, among friends of family, but elsewhere I won’t use it, though I know it’s quite a neat and polite shorthand overcoming the binary choice between ‘What?’ and ‘Pardon?’
Why that is depends on context: if I’m networking or something, it might be the first time I’ve met that person. I might have to explain, ‘I didn’t catch how long you’ve been working at XYZ, I’m deaf by the way,’ because (a) ‘I’m sorry, I’m deaf’ can sound as if you’re apologising for being deaf, and I’m not apologising for an intrinsic fact about myself; and (b) the last thing I want is for people to get flustered or give up talking to me or start to ask me questions about being deaf or the whole gamut of reactions I’ve had from a lifetime of telling people that I’m deaf.
Similarly, if I didn’t catch what the checkout lady has said at the supermarket, because they’ve changed their usual spiel, or she’s talking at the pad or while scanning, not looking at me, or this particular lady is nice and chatty and making conversation, I’ll just say, ‘What was that?’ with an enquiring expression. I don’t need to tell her I’m deaf, we both just want to get through the process efficiently. I notice more retail staff have had deaf awareness training, and they’ll make eye contact and repeat or sign ‘Thank you’ at the end of the transaction.
In other languages I might have to convey the fact I’m deaf first and ask them to repeat, and that’s where the enquiring expression comes in very handy as it seems to be universally polite: it conveys that I’m not misunderstanding you because I’m English per se, I didn’t get what you said because I’m a deaf person who doesn’t lipread your language at that speed particularly well! Making that effort in the local language is generally received well.