Green Bay at Atlanta = Green Bay, 24-22
Atlanta has the best record in the NFC and the second best in the NFL, at 13-3. Green Bay is a more modest 10-6. Never losing by more than 4 points and having a hefty 148-point differential between points fielded and points allowed, they're better than that record indicates. But are they better than the Falcons, who have a solid 126-point differential, and are a game-winning machine? That is the question.
The Falcons have slightly more points scored per game, while Green Bay has allowed less points per game. No real edge there. Green Bay wins in total yards achieved and total yards allowed, and more pronouncedly in passing yards and passing yards allowed. Atlanta wins in both rushing offense and defense. Overall, in the yardage category, I'd give Wisconsinites a slight edge.
In their one meeting this year, the Falcons won 20-17. It was a nail-biter decided in the final seconds that could have gone either way. Atlanta has a 7-1 home record this year, while the Packers are a measly 3-5 on the road. So the field is definitely advantageous to the Falcons. Still, this isn't as bad as it looks, as the Pack only loses by tiny margins; no venue has been futile for them.
The teams have only had two common opponents this year. The Falcons lost to the Eagles on the Road, while Green Bay beat them twice on the road: once in the regular season, and once in the playoffs. Both teams beat San Francisco, the Packers by a larger margin. Green Bay wins this small category.
Most of these teams' games were against "uncommon opponents" (i.e. not faced by both teams), 13 of 16 total games. Since direct comparisons are scarce for these teams, we'll have to look to these games for super indirect comparisons. In these 13 such games, the Packers went 8-5, while the Falcons were a dominating 11-2. Also, the Falcons had a slightly better average point differential (+ 10.38 versus + 9.69). However, the opponents Atlanta faced in these 13 games were somewhat inferior to the ones Green Bay faced in theirs. If you look at the average final season records of the Packers' unique opponents, it was an even 8-8. While for the Falcons unique opponents, it was 7.54-8.46. The two teams' opponents were pretty similar on total season defense (Falcons' foes being 6 points harder), while the Packers' foes were significantly stronger on total season offense (by 33 points). Neither team had a very tough journey. Still, 11-2 is significantly better than 8-5, so even if you handicap it to account for weaker opponents, I give the Falcons the edge here.
Another way to examine things is to see how each team fared against winning teams, and against losing teams. (I define "winning" as an ultimate season record of over 8 wins, and "losing" with a final record of under 8 wins.) Green Bay faced 7 "winners" and 9 "losers", while Atlanta faced 8 winners and 8 losers. Atlanta cleaned up against losers, taking 8 of 8 games. Understandable, given they got to face the Sisters of the West and the tragic Panthers. Green Bay faced plenty of chumps too, such as Buffalo, but not as many. They beat 6 of 9 losers, having mysterious losses to teams like Washington (who bafflingly also beat the Bears, and the Eagles once). Against winners, which is what we care about, the Falcons took 5 of 8 matchups, while the Packers took 4 of 7. The Falcons have a narrow edge there, though point comparison tells a different story: against "winners", Atlanta actually had an average point differential of -0.25, while Green Bay had an average of +5.86. Thus, I'd rank these teams as about even against winners. So no edge here.
Now for the quarterbacks. Matt Ryan and Aaron Rodgers have similar stats, with Rodgers slightly better in most categories. However, Ryan does have a better TD/Int ratio (over 3, very nice), and he's better protected, barely getting sacked at all. One area where Rodgers dominates is rushing; he's a regular track star, while Ryan runs like a little girl with peg legs. Rodgers also has the edge in playoff experience, albeit with a small sample size. He's been godly in his two career playoff games, while Matt was mediocre in his single playoff game in 2008, and that was against a Cardinals' defense which was very bad in the regular season. Still, that was in his very first season at the green age of 23, so I really can't judge him harshly for that. Nonetheless, the Man from Chico has demonstrated an ability to step things up in the playoffs, while Ryan is more unproven in this part of the calendar.
If Green Bay can shut down the rush, they'll force the Falcons to test their awesome pass defense, and net some 3-and-outs and perhaps interceptions. If not, they'll have to hope their offense can match Atlanta's potency tit-for-tat. Avoiding excessive false starts in front of a loud opposing crowd will be necessary to achieve that.
Based off of stats, I'd have to favor Atlanta slightly. They beat pretty much everybody, including the Ravens, and came close to beating the Steelers; the only game they weren't competitive in was at the Eagles. But from my posts here for the past few weeks, you can tell I'm captivated by Green Bay. They have an awesome points scored/allowed differential (second only to New England) coupled with a modest record that doesn't reflect it and a measly sixth seed spot -- all of this makes them desirable underdogs to root for. Not as fun as the 9-7 Arizona Cardinals from two years ago, but still compelling. Furthermore, they made a valiant stand against the evil Patriots, who had just finished obliterating the Jets and Bears in prior weeks, doing so on the enemy's home turf with backup quarterback Matt Flynn. This was impressive both in showing the Pack's bench depth, but also distinguishing them from other teams with similar records (New York and Chicago come across as pretenders with no chance of winning it all, unless New England suddenly decides they fancy golf or square dancing more).
Both the Falcons and Packers have arguably improved as the season progressed. Atlanta went 6-2 in the first half, and 7-1 in the second half. Green Bay was 5-3 in both halves, but two of their losses in the second half occurred in games in which Rodgers was partially or fully absent. Had he been in the entire games, they very well could have been wins. Also, as other posters here mentioned, Green Bay has improved their running game, becoming a more balanced team than before.