I'd probably steer you towards one of the DSLR's (or the Sony equivalent A57). The F3 is a nice camera, but it doesn't have a viewfinder, and its focusing system isn't as up to the task in low light as the others. The Canon and Nikon have the advantage of very broad systems behind them. If you like to use the rear LCD a lot though, they are quite slow to use in that manner. In that respect the Sony is a much better choice; it's as fast using either the viewfinder or LCD. The A57's viewfinder is electronic like your HX100V; the Canon and Nikon have optical viewfinders. If you haven't already, you should try both types out.
I am looking to upgrade from my current Sony cybershotSony Cyber-Shot DSC-HX100V to an entry level DSLR. I have very active twin toddler boys and I want to take pictures of them in action without being too weighed down by a bulky camera.
I've narrowed down my choices to the following, according to my budget of around $800:
1. Sony Alpha 57
2. Canon EOS Rebel T3i 18 MP
3. Nikon D3100
4. SONY NEX-F3
I would greatly appreciate advice on which camera would be most appropriate to meeting my needs.