It's interesting to hear people's different takes on Columbo, ie. is less more? By not revealing too much have the writers and Falk added to Columbo's persona? Or has this reluctance to divulge much in the way of "concrete" background information,left him a little bit of a stereotype, a bit of a cardboard cutout that seemed to be so popular back in the days of 70's tv.?
I don't think so.

I think Ted makes a good point when he says that the ongoing mystery in Columbo, is Columbo himself.

His character is a mystery because he himself is a bit of an enigma. It's one of his tools, it puts his adversaries on the wrong foot, keeps them on the hop. His reluctance to share any info on his wife, his children, house, well that is a realistic attitude for a man who deals with murderers on a daily basis.
He stays in charge of his emotions because he is a professional, and as he mentions in "Columbo goes to College", there's no point in going and blabbing about things till you're ready.

I understand and agree with what's mostly been said, but what it all comes down to (to me) is personality.

Which character do we feel more drawn to - and this is a fundamental point regardless of scripts, plots and actors.

I enjoy Monk, but I can't feel as drawn to his character as I do Columbo's. I took to Columbo's character straight from the beginning and welcomed him with open arms whereas Monk's character I feel I hold at arm's length.

Columbo's early scripts are fantastic whereas Monk's are just very good - IMO.

Also, good old Columbo didn't have a sidekick - unless you count his beloved dog ;)