I voted bored holes. The only times I might staple is when I have just one run in a crawlspace that is long and running perpendicular to the joists, or the joists are insulated, and ofc if the roof in engineered trusses. In VA we are allowed to run small NM cable perpendicular w/o running boards in crawlspaces, but I find on remodels that jobs done this way look like absolute garbage - cable piles up and is just a mess. Even three quarter million dollar homes are not immune to this.
I'd rather carry a cordless drill with a sharp 7/8" spade bit into a crawlspace than a hammer and bag of stackers/staples, the latter of which always wind up all over the place. Old wood bends staples rather easily, and hammering while on my back, I always wind up with stuff in my face. Drilling is quieter too, which some HOs appreciate. ofc I staple where I have to, and if I'm running parallel with the joists, I'll staple, but I dont saddle the wire under any beams - I'll drill a hole thru the blocking and continue.
The only drawback to bored holes is woodchips, which can take a while to clean up when the HO has stuff everywhere in unfinished basements. I find taking a small box and holding it under the TJI/joist where I'm drilling to catch the chips/dust to be much easier to clean up than shop-vaccing everywhere.
Short story: a guy I used to worked for was almost phobic against drilling holes. I had to run two 10/2 NM about 35' from the panel to outside wall - straight shot across the joists, which had to be drilled. I started to drill, and he yells at me.
He wants me to make a 90* bend from the panel, run the cables 15' down the joist, another 90* turn out to the open truss framing across the deck (which had no boards on it at the time), 90* turn back (15 more feet), then another 90* turn to the exterior wall. 4 extra 90s, and 60 extra feet of wire. He said boring holes "took too long". I explained to him that 60 extra feet of 10/2 would cost about 2 hours of my labor, and at best it would take me 10 minutes to drill 20 some holes in the 10' ceilings. I also could drill and pull wire with only moving the ladder once. Despite saving him money (and time imo), he still wasnt happy.
Had we done it his way my second cable pull would have wound up about 3' too short, requiring it to be pulled back out. Same guy also had me pull all of his 2nd floor homeruns up to the attic and back down, instead of down and thru the 1st floor joists, because we wouldnt have to drill in the attic... then complains we used too much wire. Well, duh, when you use an extra 12-16' per home run, that's what happens.