Yeah, I don't understand the mentality of "but we have xyz feature"! Its rather tacky and I'm not sure if it ever worked. There's a reason why Meerkat has fallen out of favor and its not because of a single feature. Periscope has what "304 million monthly active users" potential users because of Twitter alone. That's hughmongous! Also, the name Meerkat is not fun. Reminds me of a Ferret for some reason.
Facebook has already released live streaming for celebs. Once that catches on, Periscope will be reserved to just another feature that Twitter uses.
No one's going to win. Its just an enhancement of a service that's long due. I do think, however, that the Meerkat boys will be fine. They can just have FB write them a check and be acquired (which I believe was the intent anyway).
Twitter on the other hand, if used wisely, may help their business model since more and more people will be active on their platform because someone's on there acting interesting. (Expect to see 1,000,000 #WSHH tags on Periscope soon.)