I was just in both places last month. I spent three nights in Copenhagen, two nights in Malmo and then continued on to Gothenburg.

I had one full day in Malmo and that was enough for me. Not really much to see and do IMHO, but I'm a New Yorker and prefer urban environments.

You could stay in Malmo to save money and travel back and forth to Copenhagen, but personally, I'd rather stay in the city I'm visiting. I like to go back to my room in the early evening to relax and freshen up before dinner. You really can't do that if you're staying in Malmo unless you have dinner there. It is definitely cheaper - I stayed in the Malmo Hilton for less money than I paid for a lesser quality hotel in Copenhagen - but for me, it was worth the extra expense to stay in Copenhagen.