I have an MSW and an LCSW license and was a social worker for many years, including several years in hospital social work. I'm now in an accelerated BSN program and will (with any luck) graduate next year.
In talking to people about this same question as I prepared to change careers, the two options that generally come up are 1) hospital case management, if you're interested in that (as you know it's very different from what social workers mean by 'case management' - it's more along the lines of 'utilization management'/insurance authorization stuff), and 2) working in psych.
I've never seen a posting or heard of a situation where a job requires both degrees, but if you had a clinical focus in your MSW you will have much more psych training than the average new RN. If you had a community/outreach/organizing focus in your MSW, you will know a lot about how community resources work. That's not to say you'd get paid more or hired differently, but the knowledge would be useful. I'm also finding that the nursing model for assessment, and their version of intervention plans ('nursing care plans
') are very similar to what's taught in social work programs. So you'll have a head start in your Foundations course.