What's more of a downfall to a chess player underestimating his opponent or overestimating tactics?

Underestimaitng your opponet I guess, I have lost many games that way.

That's like asking whether LSD is worse than meth; Just don't do it and it won't matter.

I've suffered terrible losses at the hands of both, but the former is worse imo.

One of the first steps to playing chess successfully is learning to play the board instead of the opponent.  Playing the opponent means you will give him too little respect if he is lower rated, and perhaps too much if he is higher than you.  Either case is destructive of your playing ability, as you should be choosing the best move at each turn, not thinking about the opponent.

So while it is quite deadly to either overestimate or underestimate the opponent, or even to consider his relative strength at all during the game, this is a weakness more easily overcome than overestimating your tactics.  I vote for the latter.