As others have already pointed out, Nikon also has a 24-70/2.8. Since your question stems from switching to full frame, that's what you probably care about.
As a preface, the two lenses are very similar on APS-sensor cameras. The Canon seems a bit sharper toward the short end, while the Nikkor is a bit sharper toward the long end. For that situation, it's mostly a question of which end you tend to use more.
On a full frame camera, the same isn't really the case. Like most lenses, they both get softer toward the edges on a full-frame camera -- but the Nikon doesn't lose as much quality as the Canon. As on APS, the Nikkor is at its worst toward the short end, and anywhere from about 35-70 it's quite good across the frame, even wide open. The Canon does really well around 35-50mm, but gets pretty soft at the edges when you go toward either the short or the long end.
On APS sensors, it's pretty much a toss-up. On full-frame, at least to me, the Nikon seems to be a better lens -- not by a huge margin, but better nonetheless.