While it's true that DC has used the Greco-Roman (I can never remember which names are Greek and which are Roman - but, then, neither can most comic book writers; I'll just say Greek for the rest of this) gods far more than the Norse gods, and Marvel has used the Norse gods more than the Greek, I'd say it's also true that Marvel has used gods in general more than DC.
First, to be fair, I think Marvel's first book to feature a god came out in the 1950s - and that was Venus. It didn't last long (not much did, at the time), and she's only rarely been seen since (the 1970s Champions, and technically Agents of Atlas), but she counts.
Perhaps the biggest factor has simply been that Marvel has been more prone to have comics starring gods from either pantheon. The Greek gods are part of Wonder Woman's backstory, but really only became a prominent part when George Perez rebooted the character in the mid-1980s. The Greek gods are also a part of the Fawcett Captain Marvel's background (S for Solomon is the only part of SHAZAM not tied to a Greek character of some sort, mostly gods or the like), but they've only rarely been a part of his actual stories (most prominently in the Trials of SHAZAM mini-series in the 2000s). To the best of my recollection, Hercules Unbound (a twelve issue series from the 1970s, set in the future in thye vicinity of the Atomic Knights and OMAC) is the only DC book where the lead character was a god. (Yes, I'm ignoring the Diana was the Goddess of Truth for a period of time).
Yes, Thor was the first god of the Marvel age. But it was only a few years before Hercules and the Greek gods showed up.
Hercules was the tenth person to become an Avenger (yes, I'm ignoring Wonder Man and Swordsman's stints, as both were intending to destroy the group from within). He's been a recurring guest character in Thor, has had at least 4-5 mini-series, and (to date) 3 on-goings. Ares has also been an Avenger, and has had multiple mini-series.
All that said, it is true that the Norse gods have been more prominent in Marvel's comics, and the Greek gods in DC's.
One factor here may simply be that multiple pantheons are somewhat redundant. Need a god of lightning for a DC story? Sure, you could use Thor - but they've already got Zeus as a firmly established character in their universe, so why confuse things? At Marvel, what would make a Hercules book unique and different from Thor? (Thor and Odin have had father/son issues on a number of occasions, so the severely dysfunctional aspect of the Olympian "family" is sort of already in play, if not played out; though, personally, Olympus as a divine soap-opera/reality show seems like a vein aching to be mined)
I suppose geography could be involved as well, at Marvel. The Greek gods lived on a mountain, in Greece. The Asgardians realm had eight worlds beside Earth - lotds more room to spread out and have adventures.
However, I suspect the best reason as to why the primary focus is on different groups is a matter of the interests of the creators involved, and the relative familiarity with the two pantheons.
In english, at least, most of the days of the week are named for Norse gods. But, their mythology is not as prominent culturally as that of the Greeks. Icarus and Daedalus; the Iliad and the Odyssey; heck, Zeus' tendency to turn himself into animals and get it on with mortal women (which I did not learn about from the comics!). There was a series of movies feturing Hercules in the 1960s.
A lot of our word roots come from Greek and Latin, and some of that ties into mythological tales. Narcissus, who couldn't get over his own looks, leads to narcissism, for instance.
So, William Moulton Marston was interested in creating a female warrior character. And the word for a tall, strong, aggressive woman? She's an amazon. Why not take that back to the source material?
Captain Marvel used a magic word to give him mighty powers. As the Greek pantheon was better known at the time, and were in the public domain, they used those characters to power him up.
Another answer quotes Stan Lee as saying he went for Thor and the Norse pantheon when "creating" a god, because they were less well-known. I don't see a reason to dispute that. And, as mentioned in the comments, Kirby had already been involved with stories featuring Thor.