E-m5 vs. Sony Rx1

I agree. Both models of the X100 may be better choices than the RX1 for the simple fact that they have built in VFs, the excellent hybrid OVF/EVF.  The original X100 has superb IQ, with a cracking 35 f2 lens (23mm x 1.5x crop factor) and beautiful Fuji colors, but the new X100s should be even better because of significant improvements to AF (see next paragraph).

The new X100s is getting the X-Trans sensor without an AA-filter (found in the X-Pro1/X-E1), on-sensor PDAF, and all kinds of goodies like an improved VF with a digital split image MF, and focus peaking.  It's should be a heck of a camera, and will save you a ton over the RX1.  Keep in mind, that to add a VF on the RX1 add to the cost and add bulk. The X100s likely won't have better IQ than the RX1, but it will be more useable camera with great IQ for much less money.

Anyway, for a second "walk-around" camera, I cannot think of too many better choices than an X100s.