Playing a dual auto attack berserker, and something kind of important for your gear selection is understanding what determines execute speed. If the main hand weapon swings it's that weapon's speed, if the offhand swings it's the offhand speed, but what is it when they both attack?

The wiki claims that when executing, your character waits the time of the slower weapon https://torchlight.fandom.com/wiki/Execute , this is misleading. I have seen other people say it is based on the faster weapon, also misleading, and other people say it alternates based on whose turn it was to swing, you guessed it, misleading.

IF your execute chance is BELOW 100%:
I believe that you begin by executing according to your main hand speed, and this continues until you fail to execute (you chain several main hand speed attacks, not taking turns), at which point it switches to your offhand speed, and this continues until you fail an execute roll, at which point it is back to the main hand etc. Basically it alternates in chains and not every other attack. If you don't have execute chance maxed this makes pairing weapons of wildly different speeds very janky (assuming your execute is still high enough to matter), one moment you're a chain saw, the next fight you might be dragging your feet. Side note that if you intentory yourself to be just one handed and attack, the execute speed resets to be governed by the main hand (but who has time to hotswap?).

IF your execute chance is at the 100% cap:
the execute attack speed (and therefore all your attacks) will be governed by the main hand weapon speed in normal play. If you followed the previous scenario, this is no surprise: it starts by following the main hand weapon speed and never stops, because the execute roll never fails. This remains true if you stop attacking and start up again later. The only way for this to not be true is if you start with a gear setup that doesn't have 100% to execute, attack in place until the speed switches to governed by the offhand, then don your 100% execute equipment - in which case, it will remain governed by the offhand, perhaps until a loading screen or something, I didn't test that.

So if you cap execute chance mismatched weapons are preferred: you want speed in your main and heavy hits on the offhand. Technically to min max things like stormclaw that are based on weapon damage (as opposed to dps), you should use different gear to switch the execute speed to offhand by attacking in place, then put your heavy hitting weapon in the main with the 100% gear; but that's probably too much work for every single combat zone.

If, like me, this question has bugged you, hopefully this helps.