This would be an interesting matchup. But because of the potential plans either team could enact, there's really no way of asserting an opinion with any kind of clarity.
The flippant "{character} stomps" comments are painful.
If we really want to break this down: Magically, Constantine likely has the edge. Doom could match a lot of what he does, but Doom's big claim is his tech + magic. Reed has MacGuffins lodged in orifices for rainy days, and it's hard to match him feat for feat on tech regardless of who you are. That goes for New Gods as well. Added to Doom, I'd give them the tech edge.
However, since this is a forum fight where CIS is defaulted to "on" we have to account for it. And Reed/Doom aren't going to work well together. Even beyond that, team DC's respective expertise compliments each other a bit better. Some of Doom and Reed's expertise is redundant, given the other's presence.
In a battle where every one of the characters has abstract upper limits, given prep, anything said comes with a heavy grain of salt. But if I'm handicapping it, I'm giving a slight edge to Metron/Constantine. They also come with a "higher floor" as the saying goes, because the Mobius Chair would wreck shop in a non-prep battle. We can cite vague prep machinations all we want, but if either side underwhelms with their final product, so to speak, or if the prep comparison is largely a wash, the base powers of DC are higher. Obviously either side could win, but that's how I'd lean.