The best way to answer this question is with an "don't care". At this point every team you face is going to be good and it's just up to you to beat those good teams in front of you. For all the pieces of information we parse figuring if the Nats match up better with Team A or Team B, it can all go out the window with one bad start or one hot batter, especially in a series where it only takes 3 games to win it.
That being said - we have to spend our time between now and then doing something, don't we? So without going overly into stats here's what I feel.
The Cardinals are good. The Braves are better.
The problems with the Braves rotation are a bit overstated. Yes, Medlen has been great and they've won all his games, but they scored more runs for him than any other pitcher. Maholm had a bump in the road in early September, but has had a decent last 3 games. Minor has actually been really good the past month. Hudson is Hudson, old reliable, likely to have that one bad inning so he gives up 4 runs in 6. On the Cards side Wainwright, Lynn, Garcia are just as good, but they are likely to use Carpenter who is a complete wild card, since he's only started 3 games this season. Is he really fine?
At the same time the Braves bullpen edge is too highly thought of. In the second half the difference between the Cards and Braves comes down a great deal to a lack of home runs given up. The Braves gave up a silly few - like 9. So while I do think the Braves have a great pen the Cardinals isn't that far behind
The Braves are ok. The Cardinals are good.
The Braves line-up was flying high but in the 2nd half it really was exposed as a have and have not situation. If you could get through the Prado-Heyward-Jones-Freeman part of the lineup, which was good but not great, the rest could be a cakewalk. McCann, who will start most games, is a shell of himself due to injury. Bourn is MIA. They have no SS worth putting a bat in his hands. Uggla is Uggla. The Cardinals on the other hand have Molina, Freese, Holiday, and Craig hitting as well as the best Brave since the All-Star break, and Jay and Beltran are no slouches either. They do have a middle infield issue (no Kozma isn't this good) so that 7-9 is real easy usually, but you aren't getting through their middle hitters as much as surviving them.
The one thing though that keeps the Braves from being beaten soundly in this comparison? The Cardinals don't walk at al the Braves have a couple guys. In all honesty though neither see a lot of pitches.
I think Fredi is dumb dumb dumb. The Braves haven't given him much opportunity to show it this year but I can see a crucial 8th inning 1-out situation be left to someone other than Kimbrel because "who would save the 9th if we got there with a lead?". I don't know anything about Matheny other than he's not Fredi.
I'd expect the crowds to be equally as raucous, it is the playoffs, but anecdotally you have to give the edge to the Cardinals. Add in it's a longer flight, different time zone, and a stadium the Nats don't see as often and you get the feeling that coming away from St. Louis down 2-0 is more likely that coming away from Atlanta down 2-0.
As far as the last series went though, whatever psychological advantage that give would have to be stronger for the Braves. They swept the Nats and beat Gonzalez in the process. The Cards did pound the Nats recently but pounded Detwiler and Jackson, guys they might see combined once. Sure they crushed ZNN hard but that was a month ago, and he came back to pitch fine against them last time.
All in all I guess I'd rather face the Braves, the familiarity with the team, the lack of a strong offensive threat. I think the Nats could simply out pitch the Braves, winning games 4-2, 3-0. The Cardinals is more of a situation where the Nats would probably have to out slug the other team, and while that's possible, I don't think that's the Nat strength. It's an offense that feels like even facing a good pitcher would be hard to shut out, but would not prone to knocking him out.