"sneak peeking" is not good grammar, in my opinion. "sneak peek" is a noun and you can say "he's taking a sneak peek at me" or "he's having a sneak peek at me" "peeking" is also ok e.g. "he's peeking at me" However, both of these imply a short look. Also, "sneak peek" is often cheeky or fun. You might have a sneak peak at a movie before it is released, by watching a short part of it. Or you take a sneak peek at someone's diary or exam paper. In contrast "watching" implies something longer e.g. many minutes, hours, or even regularly watching you over many years. "He's secretly watching me" is either very romantic or something where you should call the police!

If he's watching you and thinks you don't know you could say 'He's spying on me!', but I also like 'secretly watching'....

It sounds better to say "He's watching me" since both neighbors can see each other, it's not secret or peeking. If one was trying to hide the fact that he was watching the other, it would sound more natural to say "He's peeking at me (through the window blinds)."