Both Sony WX1 and Sony HX5 have 1/2.4-inch sized 10.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the WX1 and HX5 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony WX1 and Sony HX5 Cameras
Sony WX1 and Sony HX5 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Sony HX5 has 11% larger pixel area (3.12µm 2 vs 2.80µm 2 ) compared to Sony WX1, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Sony WX1
or the
Sony HX5 ,
including hyperfocal distance.