Objective-C never caught on outside of the Apple/NeXT ecosystem because its biggest advantages were in the application frameworks, not the language itself. By the time iOS made Objective-C popular there were entrenched alternatives in the C++, Java, and .NET ecosystems. Swift is facing the same challenges, but against a newer generation of competitors that are much less established. It's probably still an uphill battle for Swift to gain outside adoption, but it's not climbing a cliff.
Not to mention, Swift the language itself, which is basically Rust with arguably an easier memory management model (all ARC) and Scala-like pragmatism (an OOP model built-in). Coming from ObjC, developers are showing a high level of interest in Swift. I might look it up when it comes out for Linux!
I have carefully compared the two languages and I do not see more similarity than between Go and Swift or any other language. You have yourself cited the different memory management models, and this is the main characteristic of Rust. The sole common feature is the use of LLVM.
