I recently came upon this problem in Windows where there were two shared libraries compiling with Lua statically, which caused a crash when passing a lua_State* between the two. It was fixed by linking Lua as a shared library, which is a wonderfully descriptive name for when it is appropriate to use, seeing as it was shared by the two libraries.
It will differ per project, and most libraries will say when they are better done as static libraries. If you want some definitive answer, then link everything shared until the library explicitly says to do it static.
In the case of choosing static or shared, the difference in code execution speed will not be great enough to make a difference. There are some link-time optimizations that can happen with static libraries, but I wouldn't count on that bringing you from 30fps to 60fps.