>>33772051" sits on the other side of Micro 4/3 of your APS-C, it's not very comparable unless you've got a nice wide aperture like 1.8-2.8. The RX100 III/IV are worthwhile because they're the equivalent aperture of a fairly good APS-C zoom (f/2.8-~5.0) with a good electronic viewfinder included.
Here's a secret, long zoom ranges are shit. Prioritising long zoom ratio means compromises such as significant complex distortion, bad light transmission, loss of contrast and tiny aperture well within resolution loss to diffraction territory at the long end. At 250mm on the TZ100 you're at f/16 equivalent, well into diffraction territory for a 20Mp sensor (although you won't be able to see it since the image will be NR'd to shit because so little light makes it through the lens.)
I personally wouldn't buy a camera of any description where fixed lens has a maximum aperture somewhere in its zoom range of greater than f/8. Get an LX100, Some kind of 3x zoom 1" camera, or even better a fixed prime compact like the X100 or DP2. Such cameras actually can present most of the visual promise of an APS-C dslr in a small form factor (although obviously without the same feature set, outside the later RX100's which have an insane data throughput rate for some reason.)
