DSC-TX55 broken - what to go for next?

[S6PNJ]

My Sony DSC-TX55 has died with a broken LCD screen so it's time for a new camera. I have a budget of up to £350 and was wondering what the PH knowledgeable people would recommend.

Ideally I'd like a compact/supercompact camera so don't want anything too big. The Sony was just 13mm thick but I don't think I'm going to find anything as thin again.

I've been considering a Sony RX100 II as this seems to be within price range, but not sure if I should be looking at anything else? Generally, there are no specific features I need (not bothered about GPS/WiFi) but I would like image stabilization.

I already have a Canon digital SLR so I'm not looking to fill that gap.

Any suggestions/recommendations please?

[S6PNJ]

Any more suggestions as to what else might be worth looking at please?

[S6PNJ]

It's going through as an insurance claim (accidental damage) and I've been offered a Sony HX90V as a replacement. The question now is do I go for the HX90V, take the cash settlement and get the RX100 or something else?

Also, following a quick look - what's the difference/benefit of the RX100 II over the RX 100? I can't see anything except for a higher light sensitivity on the RX100 II and I don't think I'll be needing that