Hard to say. There isn't a lot of direct competition. Smugmug probably comes closest (and I see their current pricing structure again makes it reasonable for non-professionals which it wasn't for a time). It really depends on how many people pay for a premium ("pro") flickr account which Yahoo seems to have been fairly ambivalent about collecting over the past few years.

Personally, I'd find it something of a bummer if flickr were to go away or seriously decay. I could switch but it would be a definite pain. (I also find flickr a great source of CC photos.)