Everybody should have a definite answer to this depends on where you have been brought up. Different dialects form the way we speak and in the end determine whether we pronounce it Mom and Mum.
Personally, I use Mom. Living in South Africa until age 8 meant I was taught to spell Mom with an ‘o‘, not a ‘u‘. Even to this day I haven’t changed the way I spell it (Even if it annoys my boyfriend – hehe).
The difference between Mom and Mum is like the difference between ‘colour‘ and ‘color‘ – the former is used widely in Britain (with the exception of the Midlands/ Birmingham) and the latter in American English. However, unlike ‘colour’ and ‘color’, there is also a difference in pronunciation. Americans pronounce “mom” with the same vowel as in “father”, while the British pronounce “mum” with the same vowel as in the word “but”.
But hey, this is a general rule and I’d love to hear how others spell Mom and where they’re from! So get commenting below 🙂