2nd Monitor - On Board Graphics Or Discrete?

I'm having a hard time finding a clear answer to this, so I thought I'd throw it out there. I have an Intel Core i7 10700 with on-board UHD 630 graphics. I also have an Nvidia RTX 3060ti. I play AAA game titles here and there. Right now I've been playing the latest Call of Duty, and possibly the new Diablo some day soon. I've had a dual monitor setup for several years through a few different iterations of PCs. I know in the past, it was best to keep the 2nd monitor plugged in to the on board graphics port and let the discrete card handle the gaming. (I don't remember the exact reason for this, but I'm pretty sure this was the case). Sometime over the years, the rule of thumb shifted to use the discrete card for a multi-monitor setup. My question is, is this still the case? I've tried both ways, and I'm not sure if I can see a difference. I will add that I like to stream music or twitch videos on the 2nd screen occasionally while I play, which could potentially add to the load on whichever card it's plugged into.
Thanks in advance!