Watches: this summer I went looking with roughly the same criteria. I found lots of compass watches and lots of solar-powered ones, but very few that had both features. In fact, the Casio SPF range linked earlier was about it. I bought one of those, and am fairly happy with it. However, it costs twice what you said you'd pay. It's physically big and I'd say it was more gadget/nerdy than "good looking". I wear it partly because of its other features, especially the down-counter which my previous watch didn't have. I'm a nerd. I like gadgets.

Since buying it I have been coming around to the view that solar power is a mistake. It still uses batteries, which charge up during the day and discharge at night. That must have a finite cycle life, albeit lasting longer than non-rechargable batteries would. I suspect now that it would better to get a normal battery watch and stockpile the batteries.

Carrying a separate compass is hugely cheaper than getting one built into the watch. However, I do find the watch one more convenient - it is one less thing to carry on my keyring. As others have said, if you know you are going to need a compass, take a proper one in addition to your every-day carry, whether the EDC be button or watch.

The SPF also has a barometer, which is potentially useful for local weather prediction. In practice, probably not. Mine draws a little graph, but it's a bit too small to use - my previous Casio did better. If you care about the weather you should probably check a proper forecast. Some models which have a barometer also have an altitude feature, which could potentially help when navigating, but my SPF goes for a depth gauge instead (which is useless to me - and its not rated for SCUBA use).

I have seen watches which showed tide times, that might be useful if you live near the coast.

You can get watches that store phone numbers and other data, but nowadays it is probably better to store that stuff in a mobile phone.

I can't think of anything else that would be "great for survival" other than general build-quality, reliability and water-proofness.