They have subtly different meanings. Both are perfectly fine sentences for a native English speaker.
"I feel I am missing something" means you have a nagging uncertainty in your mind that you have forgotten something (like the feeling you get when you leave home and you are not sure if you locked the door), or that you are not understanding something vital (like you are learning some mathematics and almost understand it, but not quite).
"I feel something is missing" is similar, only the forgotten thing is not your fault in this case. For example, the feeling you get if you taste a meal and there is not enough flavour, or if you see a Christmas tree and there is no angel on top.
I don't know which of those concepts the Italian sentence captures, though, if any!