It's a difficult question to answer, to be honest, with a lot of things to take into account.
The Wyatt family had one of those debuts where, a few douchebag fans aside, everything just seemed to click. The atmosphere was really cool, people were really into it and they had a fairly credible opponent to attack in Kane. From the vignettes and that awesome debut, they're instantly over. But that's not real overness, that's the overness that a great character gets when he debuts because he's fresh and exciting. It's great in the short-term, but he needs more time, character development and angles to really connect and resonate with the audience and get really over.
The Shield, on the other hand, are really over. Long-term over, which is a very special type of over. They still receive constantly good (and mixed) reactions from the crowd. People are still excited when the Shield's music hits. If you look at the other wrestlers that have debuted in the last year or two; Brodus Clay, Sin Cara, Tensai, Fandango, all of them were booked very strong in their first year and have gimmicks that had potential to get over. And yet, generally people don't care about those guys.
Whatever is happening with the Shield is something very special. And it's looking like the Wyatt Family has that kind of potential as well. But the thing is, The Shield's gimmick is simple and straightforward. They're a team that takes out who they feel is undeserving of the opportunities presented to them. Where the Shield really shines is in the ring, where they've proven they can hang with anyone and look good doing it.
The Wyatt Family, on the other hand, are all about the gimmick and the storytelling, which lets them get away with being only decent in the ring.
The best feuds are those where X is great in the ring and Y has a great character. That way X can carry the matches and Y can carry the storyline. That's why the Shield Verses the Brothers of Destruction would be awesome. The Shield carrying the matches against a past their prime BoD, while Undertaker and Kane stalk and haunt the Shield as part of the story. That's a great feud, right there.
The Wyatt Family are all about the gimmick, like the BoD. From what I've seen on NXT, the Family are decent in the ring, but they're no Shield. I don't think they'd be able to carry the 46 year old Kane and the 48 year old Undertaker to a great match. So while the promos and storytelling might be really great in a Family versus BoD feud, the matches would likely be meh.
So, to get to the point of my rant, The Shield are ready to face the Brothers of Destruction because they have the credibility, people believe they could win that feud, and the feud itself would just be better. The Wyatt family needs a bit more time, a bit more build up. And we need to see if the Wyatt family are good enough in the ring to carry the old Brothers to some great matches, which I'm not sure they are.