I don't expect a "better job" unless you specify what you mean by a "better job."
First, Atlanta didn't hire Zimmer for the sole purpose of upgrading from Ed Donatell. It's mostly born out of necessity. Petrino is now the head coach so he's brought in guys he likes and has worked with.
I understand Petrino has worked with him before but that doesn't make the guy an upgrade from our previous DC. I want a guy that I feel is going to be an "upgrade"=(better job).
Second, this could be an upgrade but I doubt a significant one. First the stats you show are a bit misleading. Before the NO meltdown in week 13, Dallas was in the upper 1/3 in PA, forced and recovered fumbles, INTs, net pass yds allowed, rush yds allowed, and total yds allowed. From week 14 on, Dallas was in the middle or bottom 1/3 in all those categories including dead last in net pass yds allowed, total yds allowed, and PA. Some believe it was due to the loss of their other top pass rusher, Greg Ellis, opposite Ware.
Atlanta melted down against New Orleans in week 12 so that's a wash.
Atlanta lost their best pass rusher for most of the season in Abraham.
Third, Dallas had a leg up on two very important defensive categories... opponent's TOP and negative pass plays %. Dallas was 10th best in the league in opponent's TOP vs. Atlanta 19th. Dallas bested Atlanta in negative pass plays, 9.54% vs. 8.88%. While that seems like a fairly insignificant margin it's the difference from being in the bottom half versus the top half. Also consider Dallas' meltdown in the last 4 games versus Atlanta being overall consistently average to below average throughout the season.
I wouldn't call a 1:24 difference in TOP significant and I believe that the Falcons suffered more significant injuries throughout the season while Dallas was healthier until the Greg Ellis injury.
I hope Zimmer is an upgrade but I'm not excited about it right now.