Lyft barely exists outside of the US. Uber is still on top if you take a global view.
Yeah, this is pretty key. If Uber's dominant position in the US is slipping but there's still a clear way for them to emerge on top globally and cash is the limiting concern, it seems likely they'll be able to continue subsidizing international expansion with more VC money.
[1] https://www.bloomberg.com/news/articles/2017-04-28/china-s-d...
[2] https://www.wsj.com/articles/didi-chinas-uber-raises-5-5-bil...