In simple cases, like your example, you should expect better performance with lambdas than with function pointers, see
Why can lambdas be better optimized by the compiler than plain functions?
As others have already pointed out, there is no guarantee that your call will be inlined but you have better chances with lambdas. One way of checking whether the call has been inlined is to check the generated code. If you are using gcc, pass the -S flag to the compiler. Of course, it assumes that you can understand the assembly code.
Update on Sep 11, 2018: Vipul Kumar pointed out two compiler flags in his edit.
GCC -Winline
Warn if a function that is declared as inline cannot be inlined. Even with this option, the compiler does not warn about failures to inline functions declared in system headers.
The compiler uses a variety of heuristics to determine whether or not to inline a function. For example, the compiler takes into account the size of the function being inlined and the amount of inlining that has already been done in the current function. Therefore, seemingly insignificant changes in the source program can cause the warnings produced by -Winline to appear or disappear.
As I understand this, if your function is not declared inline, this compiler flag is most likely not helpful. Nevertheless it is good to know it exists and it partly answers your second question.
The other flag that he pointed out is:
Clang -Rpass=inline
Options to Emit Optimization Reports
Optimization reports trace, at a high-level, all the major decisions
done by compiler transformations. For instance, when the inliner
decides to inline function foo() into bar() [...]
I haven't used this one myself but based on the documentation it might be useful for your use case.
I personally check the generated assembly whenever it is that important.
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