The AX100 would be a step up for you in terms of picture quality, but you would have to live with lack of physical control and fiddly menu access.
Another option would be to find an EX3 or EX1. A very good condition one is quite cheap now. And these would give a similar type of physical control as your present camera. With the advantage of card recording. You can even use SxS adapters that use mega cheap SD cards.
I went from the FX1 to the EX3, and never looked back. It is a better camera all round and produces full raster HD as opposed to the FX which does an electronic anamorphic 1440. Although, in the long run the EX1 would have been just as good and cheaper, as I never used interchangable glass.
I have gone from the EX3 to the AX100. Although this may seem like a step backwards, and it undoubtably is as far as form factor and proper physical features are concerned. The AX100 produces a better picture, for both resolution and noise. If you can live with the size of the AX and its lack of proper physical control. I would recommend you don't look any further, as its picture quality is absolutely fantastic.
Although I moan about the lack of physical control of the 100, I have started to take advantage of its physical size. I now have a full interview/doc shooting kit that all fits in a backpack, including lavs, shotgun and tripod. The shooting kit is so light, that I can get around town on public transport and be setup really quick with a client and out in a flash.