I guess you probably have already made your decision, but to pipe in, I lived in both Munich and Mannheim and I loved both. The ironic thing, I used to live in Esslingen (near Stuttgart) and found a job in Munich, which sent me on a project basis to near Heidelberg! After 3 years I joined the company I had contracted for and having lived in a 35 sqm studio apartment, which was cozy and I made it my home, I really wanted at least 1 bedroom and the prices in Heidelberg were the same. A work colleague suggested Mannheim. I lived in the Schwetzingerstadt, a short 10 minute walk to the train station and had a lovely commute by train and then later by car (A6 all the way), to work.
For city living, this was perfect: I had all I needed in my neighborhood (cafes, restaurants, grocery stores, doctors, beauty salons) or could walk to town or if needed more, a hop on a tram to one of the big malls either in Ludwigshafen oder on the border to Hessen, the Rhein Neckar Zentrum (Viernheim). Munich, everything was bit more spread out, but each neighborhood had its own vibe and feel. I rarely went downtown, but to hit up Karstadt Sport or Hugendubel. But in the end it was the price of everything that made me glad to have left Munich, though if we had A LOT of money, we would consider moving back to Munich simply because hubs is from Bavaria and we'd be closer to family.
Mannheim has a large LGBTQ community and pre-covid there were great parties at the Alte Feuerwache and other clubs like MS Connexion, but its prices are not nearly as affordable as they were when I first moved to Mannheim. In 2010, we paid 700 Euro cold for nearly 100 sqm. I'm sure our landlord is charging double that now for a flat last renovated in the 90s and built in 1955!