X10 handles better when its in your hand, as its a more traditional, or "old school" as many call it design, with dedicated dials and buttons rather than multi function "soft" keys etc as many of todays modern cameras are going to. I personally enjoy having a physical manual zoom ring for example, EC dial etc.
HOWEVER, the X10 is just not a pocket camera in the slighest, while the RX100 slips easily into any pocket and also offers better performance in almost every way.
Much better video, faster frame rates, higher resolution, lower noise, more subject isolation, better pano sweep and other perhaps gimmicky processing modes, faster AF, you name it really.
X10 though is fun to shoot when its actually in hand, but question is what to do with it when your not actually shooting.
Also at $599 for the X10, given its performance, is also sort of steep for what your getting compared to the SOny for $50 more.
All and all though rather different cameras so kind of hard to compare them directly