MN-ers are snobbish and on here you always see the same expensive places in South Manchester Altrincham, Didsbury etc these places are South West prices. But still... when I lived there houses often smelt of weed. Even in posh Hale (which is Cheshire, just next to Altrincham). People aren't getting gunned down or stabbed to death in the rest of Manchester y'know!
Also for MN-ers places with 'a lot happening' and 'good public transport' = a place with some nice restaurants, a couple of gigs , And a train station.
FWIW Reddit is a better place for honest answers OP but Manchester has more going on than Liverpool. Liverpool is cheaper, has better museums and galleries but most of it concentrated in the city centre... crickets elsewhere. Transport isn't great either - no trams.
Manchester has trams, which are quick and cheap. You cannot beat the sheer variety of restaurants, street food, events etc. It's a bit like London - you have the city center but there's also lots going on the suburbs of Altrincham, Didsbury, you can go further to Cheshire for nice countryside things. As you are Turkish no problem finding your own food here.
I would say 'safety' is the same in both cities and the rainy poster ROFL (most of the North West is rainy!) Have a Google - Manchester isn't even one of the top ten rainiest cities in the U.K despite its reputation.
Places like Leeds and Sheffield, while good just don't have the variety of Manchester and Liverpool.
Don't listen to strangers on the internet and jump straight into buying a house. Rent in Manchester or Liverpool for a bit - explore on your own terms, visit all the cities.
FWIW I live in Hyde, East Manchester which MN turns its nose up at but people are SO nice. I constantly get people stopping for a chat in the streets and shops, doors etc held open. When you bump into people and say sorry they actually REPLY BACK instead of ignoring you. And if I looked lost people are happy to stop and help.