The 2011 Nats had more stolen bases in the first half (78), than the 2012 Nats have total (76).
They are, however running smarter. 75% SB rate in 2012, 73% in 2011.
If you look at the 2011 team, after Johnson took over, they stopped running completely, only putting up 28 SB in the second half of the season.
Davey was never a running manager, at least not comparing his Mets to the Cardinals, but the 2012 Nats seem to run in ways that pressure the defense into errors. I saw it up close last week against the Braves, when guys like Uggla or the 1B would hurry plays because Nats were running hard. The Braves would hurry so much that they missed the play. I remember a likely DP in the Detwiler Sunday game, except that the SS tried to throw without really having the ball. Another play on a ball pounded into the ground, bouncing high over the pitcher and 1B and neither could decide who would field it.
Same in the Mets series, especially on that play at 2B when the Mets SS got spiked...but after he had dropped the toss from the 2B.
Not SB's, and the plays often don't show up as errors, but they are mistakes that fielders make because they have to be perfect. A play that Espinosa made yesterday on N Morgan in the 9th, but that other teams often don't make against the Nats.
(Also think of the times that guys have scored from first on a double, or gone 1B to 3B on a single. )
I don't know a stat that would show it, but I think the 2012 team is running more effectively.