I travel regularly and it is very rare not to have Lyft available. Virtually any city with >250k has both from my experience, although that could just be where I travel, I don't know.
Everywhere other than the US and Canada?
Lyft is US/Canada only, while Uber is much more global.
I'm well outside of SV, use Lyft occasionally, and never use Uber out of principle.
Whatever Uber did to paper over what news of their misdeeds reached general cultural consciousness (if any...) seems to have worked for the most part. That's a shame, since I truly believe there should be much harsher repercussions for their blatant disregard of the law over an extended period and the pain and problems it caused to many.
I suspect if the market was working efficiently, Uber would have a lot more problems and be in a much worse position than they are (efficient markets assume good information, and if people don't know what Uber's done, they can't make an informed decision).