The SEC being from "top to bottom" the strongest conference in the nation is a bit of a missconception, but so is this. The SEC is loaded from top to middle, but the bottoming teams are just as weak or weaker than the weak teams in any other AQ conference (minus the Big East, obviously), and people tend to overlook that.
The SEC doesn't field 1-3 great team every year, for the past few years, it's fielded 3-6 every year. Then usually a 1-3 pretty good teams, and then the bottom half which usually suck and don't even make it to a Bowl. Last year, Alabama, Florida, Texas A&M, South Carolina, Georgia, and LSU were all awesome teams capable of competing with most teams from any other conference. The year before that, it was Alabama, Arkansas, LSU, South Carolina, and Georgia.
I think Nebraska would actually do pretty well in the SEC… they wouldn't be great, at least not at first, but it would probably improve over time. It's a program rich with tradition and winning, and a team like Nebraska would experience a slight recruiting bump in its recruiting area because it could use the SEC as a selling point, which no other team nearby could do. Players in Nebraska and the bordering states could play for a decent team in the SEC without having to travel very far.
The SEC is the best conference. The people for and people against both tend to exaggerate how good or bad it is. It's stacked better than any other conference, but it's not solid from top-to-bottom, that's for sure.