Thoughts on Heidelberg vs Mannheim from a foreigners POV

I feel like there is a lot of different information about Heidelberg and Mannheim (probably because of people see things differently) but to my knowledge so far. Mannheim is the bigger city (300.000) and Heidelberg (160.000) but Heidelberg is way more popular and is one of the most touristed cities in Germany?, while Mannheim isn't very popular therefore Heidelberg seems more crowded and has as many bars and shopping opportunities as Mannheim? - and as many or more things to do?
I am more confused on the housing in Heidelberg which by the looks seems expensive if I don't get some of the cheap options through the university, but I don't know if these are even placed in or close to the city center and if it's only the very expensive (rooms for more than 500 euro a month) that is placed in Heidelberg city.

I feel like there is a lot of different information about Heidelberg and Mannheim (probably because of people see things differently) but to my knowledge so far. Mannheim is the bigger city (300.000) and Heidelberg (160.000) but Heidelberg is way more popular and is one of the most touristed cities in Germany?, while Mannheim isn't very popular therefore Heidelberg seems more crowded and has as many bars and shopping opportunities as Mannheim? - and as many or more things to do?
I am more confused on the housing in Heidelberg which by the looks seems expencive if I don't get some of the cheap options through the university, but I don't know if these are even placed in or close to the city center and if it's only the very expensive (rooms for more than 500 euro a month) that is placed in Heidelberg city.

Then there is of course the social, but I guess there shouldn't big difference between how it is in Heidelberg compared to Mannheim? But I can see that Mannheim offers a lot of different sports for students for free - is this also the case at Heidelberg University?

I am not definitively looking for a city with crazy and late nightlife, but maybe more just some nice bars or private parties, and then that there is some bigger events a couple of times in the semester.