When you first summon him, whoever is in your crosshairs is whom he will attack first, even if other enemies are closer. If none are in your crosshairs and you’re sufficiently far away, he may ignore them until combat commences.
During combat, if he loses aggro, move to use him as a shield; a couple shots from an enemy will wake him up.
The Sabre turret I think is a much stronger summon (doesn’t lose aggro, the one attack “just works”, and while it can’t follow you around (and can’t extend its life with each kill), the cooldown for reclaiming it and overall speed of its cooldown makes it a winner in my eyes.
That said, I think Deathtrap is way more fun to use, especially once I got the nuances of his engagements. His kills are more satisfying, and even with the Buck Up bug, I think he’s more reliable than people give him credit for, but unlike the turrets, he’s not a “fire and forget” summon.