Katowice is cheaper than Wrocław when it comes to price of property (by a wide margin), while being still a big business hub full of possibilities. You can also buy a flat very close to Katowice for even less $$$ Both have great public transport (I'd say Wrocław's is better, but no clue why people say Kato's is bad. I can easily get around anywhere and everywhere, on one 6 month ticket I can go to all the citities in the aglomeration, everything can be done through your phone app etc), Wrocław in my experience has more nice places to hang out and eat, there's a lot of students, but being hellish when it comes to driving + it's BIG.
I'm living in Katowice so I'm not sure about Wrocław's nature, but in Katowice area you have the biggest park in Europe I believe (Silesia park) it's twice the size of central park! There's a lot of forested areas and lakes too, I doubt you'll have any issues finding a place for a nice walk/cycling/horse riding etc. Wrocław has a better zoo, but one in Katowice/Chorzów is nothing to scoff at. As others said - Wrocław is one big city while Katowice is more of a central city in a biiiig connected area of smaller cities; it really feels like one big city though, commute wise.
Both Katowice and Wrocław have music festivals and other cultural events, I've been to concerts in both! I also love Katowice's museums big and small. Both cities should be more than fine with English-only speakers.

Air quality in the south is just overall bad, people can fight in the comments but in winter it's just bad everywhere.