Men, were you obsessed with your woman from the very beginning?

My friend has this theory that relationships are more likely to last if the guy is more obsessed with the girl especially at the early stages of dating.

27F, I’m currently in the talking to 2 guys (non-exclusive, both I’ve been on multiple dates with)

Guy 1 - 26M, 2mos talking, is quite obsessed, texting almost everyday, has been hinting at exclusivity, but he has gone back to his country and I don’t do long distance so it’s uncertain.

Guy 2 - 32M, 2wks talking, not obsessed, not texting much, taking it slow, intimacy not till 3rd date, it’s not the magical type of connection, but there is attraction somehow. Also uncertain.

So, which is better obsessed or slow burn? Should I just give it more time and see where it goes? Or just start fresh, and go out and meet more people?