I'm not sure it's either the most loved or hated, at least if we go by what surveys we actually have.
I know that something akin to "most hated" was taken by some agency not too long ago, though their terminology may have been a bit different. The poll was international and iirc, came from a large enough sample size. The United States did not top that list. Other nations like North Korea, Iran, and Israel were higher up than the United States.
I do have doubts we're the most loved as well, since a lot of nations do seem to criticize the United States more than most. A lot of our international actions aren't so universally loved, at least, which would make it hard to be the most loved. I do have to wonder what nation is the most loved, since the candidates I can think of still have their critics worldwide (like the UK, France, and Japan). It's not so obvious, at least to me, who can be "most loved".
I will say that the United States does seem to invoke great feelings in many people, whether that be love or hate. There are definitely people who hate us, like Iran's many "Death to America" chants; however, there are those who do appreciate us, like the recent protesters in Hong Kong waving our flag specifically because of the freedoms our country represents to them.