Well, first off, the EF 55-200mm
isn't an STM lens, nor is it stabilized. (There is an EF-M
mount version that is, but it won't work on the EF-S
70D.) So if you really meant the non-STM and non-IS EF 55-200mm, then I would say the FZ1000 is clearly the better buy.
However, if you switch to the EF-S 55-250mm
which has both IS and STM as well as a full frame equivalent focal range of 400mm, things get a lot closer. Although, I would still give the edge to the FZ1000 for 4k video at a lower price point.
Also note that both cameras will struggle "indoors under fluorescent lighting". Obviously, the 70D could do better with a brighter lens, though, whereas the FZ1000 cannot change lenses. But now you're looking at more money; probably a lot more since bright telephoto zooms aren't cheap.
HTH - Mark