Basically what I'm asking is compared to other pantheons of gods (i.e. greek, roman, norse, etc.) how do they compare? Do they have a higher or equal level of power?

The New Gods are not actually gods (as we may think of gods.)  They are beings that are so powerful and that can do so many amazing things that compared to us, they may as well be gods, and they think of themselves as such.  They simply appear to have limitless power to us.
 
That being said, I believe that it was the power of the Old Gods that gave the Greek gods (which exist in DC) their power.  This would suggest that the New Gods are more powerful than the Greeks, at least.

Some are, some aren't. I'm pretty sure Zeus is more powerful than Orion, but how he compares to Darkseid, I don't know. Superman has been looked upon as a god by many people in the DC Universe many times simply because he is so powerful compared to others. Batman mentions this in the Superman/Batman: Supergirl series when Superman faces off against Darkseid. Don't have scans right now.

I'd say the New Gods are as powerful as some other panthions, Hell Mr Mircle put DC's Thor down with not much effort. As for what one guy said about Zeus being more powerful  than Orion. That could be true as Highfather is regarded more powerful than Orion and he is a New God also. And as for what someone else said The New Gods ARE Gods they are not just some powerful alien race they actully ARE Gods, They have spoken with other panthions of Earth Gods before and are on par with them. Darkseid has also Killed off some Panthions of Gods to get there powers.