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When you move to FF your EF lenses will seem shorter. Their focal length doesn't actually change, but the 'Field of View' you will get will be wider. So your 50mm will have an normal FOV of 50mm; like it would on a film camera. On your 30D you are really seeing/saving an image with a FOV 80mm; your 30D's sensor has crop factor 1.6x. All 'EF' lenses on a crop body have more 'reach' because of this crop factor, change in FOV.
Moving to FF, the 6D, will get you more pixels, much better higher ISO usage and it's body is actually a bit lighter/smaller then your 30D. And as others have said, the EF-S lens you have does not normally work on a FF body, you will have to use it on your 30D only. With a FF body you might look at the 17-40 f4L for your ultra-wide needs.
As for the OMD, it looks like a nice small alternative, but good glass can get really expensive, with body, grip and a few fast lenses you're looking at 2.5-3k.
6D kits with the 24-105L are going for 2.4k plus tax, pretty cheap to get into FF, but given you are use to shooting with a 1.6x crop body I'm thinking a 7D might be an alternative. You'd move to 18MP, higher ISO use, much better AF, 8FPS and it's internal-popup flash can act as a master flash. You can get a used one from here on FM for under 1K and all of your lenses could be used.
I'm looking to move to FF also, I have a 40D and 10-22 with other EF lenses, and don't like to crop much; even with its very clean 10MPs. My eye is firmly on the 6D kit also. The 'reach' issue isn't a big problem for me as I shoot with film bodies years don't mind the loss in FOV, am quite use to that look.
You might bring your kit to a local shop/store and try your EF lenses on a 6D and your 30D. If the change in FOV doesn't bother you, gives you enough reach for your needs ...then FF looks good to me. BUT...if you miss the 'reach', crop factor, then the 7D or it's upgrade that might come later this year or early next year might be a better option.
Hope this helps...
Edit - Just read you post about your kids and their portraits, while bokeh is a great look, if/when your kids start moving into sports, given the 6D's AF is pretty much center point focus only; unless in really bright/good light, the 7D might be the best option...just a thought...even a T3i or T5i might work...test the 6D before you buy make sure the AF will work for you.