Willitts1989 - if you haven't got one yet, the zoom on the Olympus, whilst powerful, is not essential. You'll miss a few shots perhaps, but I'm travelling with two DSLRs and a 4/3rds point and shoot that has a fixed lens of 35mm equivalent on full frame. I use a fixed prime lens on one of my DSLRs most of the time, and that's my walk around/night set. I used foot power zoom to frame my shots rather than standing up and staying still: makes for more interesting images.
Zoom is great, but if you use your feet and imagination, big zoom is unnecessary for the sacrifices you have with it. For $100 more the LX7 will give you superior images. That 24x zoom only exists for small sensor camera's, and there's more you miss out on because of it, it's a great all rounder pocket camera but the LX7 stands above it once you get past the zoom. I'm not trying to bash the SZ31, it's a fine camera that will be preferable to many - that's why they sell well. It's down to preference, hence why there's hundred to choose from! I'm just giving you my preferences...
Sensor size makes a huge difference once you get past the small sensors of standard point and shoots. You won't use the full features of the LX7 at first, but at least if you want to move further into creative control of your images, you have that option - shooting manual modes (either fully or aperture priority/shutter speed priority - I use that for panning shots of moving things), shooting RAW for example is a huge step up from JPG, and you have the ability to post process your own final images rather than rely on the camera to guess it. LX7 gives you control, the SZ31 is ideal if you just want an image and not have to think about anything but framing. The aperture and sensor size on the LX7 means you will be able to use it at night time for superior results with less 'noise' (lower iso). Cleaner images. The sensor size means, as I mentioned before, you can get subject isolation and background defocus. That alone will give you better images as small sensor point and shoot cameras produce fairly flat looking images when subject isolation would be better - portraits for one.
Good luck. Controversial subject!