I say maintaining multiple live action versions of the same character in live action at the same time is a bad idea, in part, because it invites negative comparison. Cavill's Superman and Miller's Flash were both subject to criticism because many fans preferred their WB counterparts. It also leads to fans asking why the powers that be can't just move the guy or gal we already like onto the big screen, and it can create bad feelings when a role is recast. And I think fans would be less likely to watch, say, a Flash movie if they are sitting on dozens of Flash episodes in their Netflix queue.
Both Marvel and DC have a sufficiently large stable of characters. Both should be able to avoid putting dueling versions of the same character onscreen.