The dreaded "can you recommend me a good camera"?

I happen to also own an S100 that I'd love to get rid of. I bought it thinking it would be a step-up from my 330 but that's not the case. The lens isn't as sharp and basically it's a PITA to use. Which was really really surprising to me.

If you read up around here, you'll find reports of the S100's lens having optical quality problems. There were various speculations about why, especially because some cameras seemed much more affected than others, but Canon issued a product advisory. See:

https://www.dpreview.com/articles/2259215733/canon-powershot-s100-product-advisory

I suppose you could ask whether Canon would still fix your S100.

By all accounts I've read, Canon used an essentially-similar lens design for the S110, but had sorted out the problems by then. As DPR said in its roundup comments on the S110:

We had some concerns about the lens in Canon's previous S-series camera, the S100, but we're very happy with the optical performance of the S110's 24-120mm zoom which delivers good edge-to-edge sharpness across its span of focal lengths.

See https://www.dpreview.com/articles/2367736880/roundup-enthusiast-zoom-compact-cameras/4.

But I wouldn't pawn it off onto my friend, I'd rather sell him my backup 330. One thing to consider is, this guy is huge, he has really big hands. An RX100 would be too small.

To me the 330 HS, RX100, and S100 / S110 / S120 are all in the same size category. I like that category because they slip easily enough into most of my pants pockets and/or a small soft case on my belt. But how any given user likes or doesn't like the controls is a personal thing. For me, as skeptical as I was about the S110's touchscreen, I've really come to like it, especially for selecting the subject on which to focus.