As an owner of both the A7s and AX100 and as someone that has shot with the PXW-X70, if I had to choose one which would it be? That’s tough because although they really are very different cameras they both have strengths that are nice to have. The A7s produces a prettier picture and can be used run and gun, with limitations. I use the kit 28-70mm f3.5-f5.6 and it works well, good auto focus, smooth aperture changes etc. BUT and it is a very big BUT you need a really good set of ND’s or a strong ND fader to use it outdoors due to the extreme sensitivity. Add to that the minimal 3x zoom and it’s pretty restrictive as to what you can shoot without switching lenses and fiddling around. Sure you can add something like the new Tamron 16-300mm f3.5-f6.3 but the autofocus tends to hunt a lot more, manual focus is fiddly and you still need to mess around with ND’s. I think you need to be a fairly competent cameraman and need to be very careful over lens choices etc to use the A7s for run and gun successfully. Plus don’t forget the cost of all the extra lenses, filters etc adds up and makes the kit bulkier.
The AX100 (or PXW-X70) on the other hand really is a grab and go camera. Easy to use, great zoom range, built in ND’s. It’s quick and easy to use and may get you shots that you will miss with the A7s. But the pictures are not as pretty, primarily they lack the dynamic range of the A7s. But they are very easy to use, so well suited to those that are full auto shooters or rely heavily on auto functions to keep life simple. The X70 has much better ergonomics than the AX100 but is a bit more expensive. Both are very compact packages and as you don’t need to buy extra lenses or filters work out substantially cheaper than an A7s kit with a set of lenses to cover the same focal lengths at reasonable apertures.
Anyway, if I had to give up one of mine (A7s or AX100), for me it would be the AX100 that would go. I would be prepared to sacrifice the ease of use of the AX100 for the better images from the A7s. But I normally shoot manually anyway. I’m used to swapping lenses, working with ND filters etc. If you not used to shooting manually then the AX100 may be the better choice. Great images are of course important, but the best camera to own is a camera you will use. It’s all very well having fancy pictures and the ability to swap lenses etc. But if fiddling around means you don’t use it very often, then there is no point in having it. You would be better off with a camera that you will be comfortable with, that you will use regularly.