In part it will depend on the body on which you're intending to use it. I'd already read about the image stabilization question (Panasonic does it in the lens, Olympus in the body, so mixing can lead to no stabilization or the two systems "fighting" each other - though (on an Olympus) either or both could be switched off).
Thanks to your question (and Startpage), I've found that there's a whole list of possible issues.
If you have an Olympus, there would be some advantages to the Olympus lens. If you have a Panasonic, it might be easier to use their lens. Generally, though, either can be used on the other, and it sounds from this as though the later and/or high end models are able to work around some of the issues raised.