Both if you can.  They all bring a certain uniqueness to the Endurance Run experience.

I guess a good compromise, judging by everything that's been said, might be:
 
1ST HALF (1-34): VJ 
Intermission: BR15, 21, 30
2ND HALF (35-41): BR
 
Personally I prefer BR because Brad is probably just as bad at combat as I am and Ryan seems to genuinely respect the story, but if you like VJ's goofiness and can't stand watching people be bad at vidjagames, you could watch VJ for the first 30 or so eps and then BR for the rest of it.  Like people said, BR had better reactions to things, but those are scattered across episodes so you'd kind of have to track them down.  But I'd say the last part of the ER was definitely BR's territory for the sheer insanity of everything (also VJ seemed to get confused by aspects of the plot which bugged me, where Ryan pretty much picks up on everything right away).  
 
Of course, there's no reason not to watch both.
 
For those of you who've seen everything already:

Honestly... both weren't that exciting, and there were a bunch of moments in each (mainly the wall lady parts) where things became really painful to watch. If you still really, really want to watch the Endurance Run, I'd say go with VJ, but you'd be better off just rewatching the Persona 4 ER. 

Hmm... I don't want to watch the P4 ER before I play that game, which might be a long time.  Why did they choose it for the ER?  Is it as crazy as DP?

" Hmm... I don't want to watch the P4 ER before I play that game, which might be a long time.  Why did they choose it for the ER?  Is it as crazy as DP? "

VJ

Both, they're both awesome

Dude.....yeah. There's a reason its much more popular then the DP ER(though I still hold that's partly the guys' fault!).  Also, their original reason for starting the Endurance run 1 was them wanting to play Persona 4 but nothing having the time to do it.  haha. back then, people weren't that sure that they were going to keep playing it because it hadn't caught on yet with the audience. I'm convinced if they entered DP with the same mentality as P4 they would have(sadly) dropped it. "

VJ! It's the classic. After you've finished, you might want to go back and watch BR though. That's what I'm doing pretty soon.

" @Jeffsekai said:

" neither. "

That sounds like a great idea, I love you. <3 "

BR, the VJ run felt too much like they were trying to make jokes all the time which put me off badly.

Ryan and Brad get into it more after a few early episodes of not giving a shit, plus Ryan is the funniest member of the GB crew by a fucking mile so....you're in for a treat with that one.

VJ... You know what to expect from them if you watched the P4 ER.
 
BR is hard to watch thanks to Brad being Brad at games.

VJ, however I didn't watch BR, so i am biased :)

I ended up watching both. I not necessarily saying you should do that though. I'm a bit insane. 
 
BR seemed to be more into the game then VJ. Brad's combat was funny but sometimes annoying (final boss I'm looking at you). Both have there good moments though. 
 So what I'm trying to say is that I can't decide, and thats why I ended up watching both.

" @mutha3 said:
   I wonder how long they'll take to do another ER.  They seemed pretty blown out after DP.  Unless that's how they acted after P4 as well? "

They'll add a team every ER.
 
Next Season: Team DaveDrew

VJ

Both

VJ.  
 
Brad's incessant bitching ruined their playthrough for me.

I know this is super late, but I just wanted to add my personal opinions to anybody reading this in far off future land. I personally preferred Brad and Ryan. You're going to have to watch a little of both before you really know for sure. If you are invested in the story of Deadly Premonition, I would go with Brad and Ryan. If you are watching only for the Giant Bomb personality  go with Vinny and Jeff. Also, if you aren't very tolerant of Brad "pulling a Brad", then I would advise against it.  
 
If you watched the Persona 4 Endurance Run, think of like this: Did you enjoy Vinny and Jeff playing Persona 4, or did you just enjoy Vinny and Jeff? Vinny and Jeff are funnier than Brad and Ryan, but they are no where near as invested.