Of the two teams I think Prime Wardens probably takes it by sheer firepower, however it's tough to say. I agree with earlier posters that F5 probably would use better teamwork and tactics so they might be able to overcome the initial disadvantage, but I think the fact that PW has two more heroes that can fly could present a significant challenge in terms of the FV keeping the matchups in their favor and could possibly allow them more freedom to choose who each fights against.
A couple of disclaimers about my thought process first:
1) I've never seen Captain Cosmic's deck, but I'm imagining him as a scaled-down Green Lantern (all DC heroes are way too Overly Powerful to be directly compared to SC heros).
2) I'm imagining the hero fighting sytles as not being turned based but analogous to what they can do in a single turn, in terms of pacing and how many things they can do at once (the obvious exeption being Tachyon, even though she plays a lot of cards per turn would still probably fight faster IRL). Meaning Wraith and Legacy are better at using two powers at once than others, and Bunker being the expert tactician and good at drawing cards is good at thinking ahead. That's how I picture the card draw mechanic, as planning ahead, because they should be able to do almost anything at any given moment and not have to draw into it.
For PW strategy I would think:
Fanatic vs. Legacy - Can match flight and has enough attack/defense to keep Legacy focused on her to buy time for a double team. Do not switch under any circumstances, even if she's losing someone else can jump in to help temporarily. She doesn't have to win, just take the F5's biggest gun out of the fight.
Haka vs. Bunker - Rush him and don't let him get set up. If Fright Train is a credible nemesis for Bunker, Haka should be too. He could also probably stand up to Tempest's attacks but I don't think Tempest could handle his offense.
Tempest vs. Tachyon and helping against AZ - Lightning might be the only thing fast enough to get to Tachy and rain/snow/hail can mess with her footing to slow her down. Against AZ can maybe help mitigate his ice attacks (although I'm not sure if his weather powers work this way) and I would think is tech-based suit could be vulnerable to lightning. He has enough Area Of Effect attacks to help against two people at once.
AA - Support the others and help where needed. He can obviously heal and protect the others and he has some ongoing and card destruction that would be useful against almost anyone. He can also deal some damage, although his only damage that would work against AZ is 1 sonic.
CC/Wraith - This is my wild card spot since I don't know CC at all. Also have you ever noticed in any multiple hero vs. villain fights in the DC universe Batman often gets overlooked by the villains and it never works out for them? I think the same thing would happen with Wraith on a team of obviously powerful heroes but we all know Wraith always wrecks the villains in the end. I'm assuming CC is fairly powerful and has some nifty constructs that can attack and defend against Wraith's attacks and at least buy time if not possibly win.
F5 Strategy:
Legacy and Tachyon would be the best at rapidly switching to help others so I would have them try to switch on to anyone who has a disadvantage. As the only flyer I'd try to keep Legacy in the air as much as possible.
AZ: Target AA since he can do very limited counterattack damage, although card destruction is a big concern. If you can keep AA focused on himself instead of helping others the PWs lose a lot of team chemistry and the FV teamwork might prevail. Can also physically slow down anyone such as CC, Haka, and Fanatic.
Wraith: I think Wraith can hang with, if not neccessarily beat, anyone. Therefore I would have her take on someone on the surface more powerful than her, namely Fanatic. If she can keep Fanatic from shutting Legacy down she's definitely pulling her own weight. Depending on Cosmic's strength he may also be a prime target to distract. Again - wildcard.
Bunker: Attack either Fanatic or CC, depending on who Wraith draws. He has the projectile damage to reach those two flyers and the defense to withstand a lot of punishment, which would be needed against Fanatic. I'd avoid the matchup with Haka since they seem too evenly matched. He could send a few bullets Tempest's way too since he has the ability to attack multiple targets.
Legacy: I would bum rush Haka and stay on him relentlessy unless someone needs help, then just fly away to give support and jump back in. Haka can deal tremendous damage but Next Evolution would shut him down completely by becoming invulnerable to melee. If you shut down Haka's offense the PWs lose a lot of firepower. He could also probably close the distance on Tempest better than anyone so if Tachyon can't get to him first he might have to go there since Tempest has too many strong attacks to be left free.
Tachyon: If she can get to him first Tempest would be a great target since he does a lot of damage but is relatively squishy, otherwise if he gets the drop on her and she can't get up close I'd avoid him like the plague. Haka is really her only other target she can reliably reach since the rest can fly and I think she's fast enough to avoid his strikes and do enough damage to draw his attention. Basically she would do anything that Legacy isn't, but I would keep both moving freely to help where needed.
In the end I think the PWs have more favorable matchups and can better dictate who goes against who so I give it to them, although it's really to dismiss the fact that the F5 is supposed to be a tactically brilliant team. They could probably come up with something I missed.