Initially perhaps, but not for long. Within a few years, I suspect SEC will surpass the Big XII, and it might be by a wide margin. The move to the SEC has huge revenue implications, and while football was the large driver, this will spill over into other sports. Basketball will be the biggest benefactor after football.
Just look at schools like Alabama and Arkansas, who I would not consider traditional basketball powers. They're both positioned to easily be top 10 programs over the next 5 years, and that's almost entirely based on money. Recruiting against them is almost a lost cause currently comparable to the blue bloods. I'd rather see Gonzaga or Villanova on a list for a guy we're recruiting.
KU will remain a power, and Baylor is positioned to stay strong, but the rest of the conference will decline. KSU has a great thing going with Tang, but it's only a matter of time before an SEC school like LSU breaks the bank to bring that mercenary to their side. UH will be great as long as Kelvin is in charge, but that may only be a few more years. It's only a matter of time before SEC basketball starts to look a lot like SEC football (and baseball). Most of the schools that struggle in football will likely take the Arkansas route and dedicate their funds to basketball. I've been expecting Vanderbilt to give up on football and just be a baseball and basketball powerhouse.