I think an archery hunt in a good coues deer area would be more exciting than a rifle hunt in a poor area. That said, archery hunting for coues deer is perhaps the greatest hunting challenge in the US.
The archery success rates are a little misleading in the sense that quite a bit of archery success is attributed to two tactics that will likely not be available to you in January.
1) It can be hot as heck during the early archery season so sitting water has produced coues deer for some very patient archery hunters.
2) Some archers that live near their hunting grounds set up and maintain bait sites...water, salt, alfalfa, cameras, tree stands, the whole nine yards. That scenario can and does result in successful archery hunting for coues deer (check local laws).
For a couple of guys to travel to AZ, bows in hand and hope to find a hot deer trail or spot and stalk a coues buck...well if you are successful that would be an event worthy of long and loud celebrations.
Regardless of success, I hope your trip is a blast.