And this isn't just one of those, "It broke the record! How can you improve on that?" things. It's also not a DC-versus-Marvel thing (I'm a DC guy). What is it? Math.
Since The Dark Knight Rises was not filmed in 3-D, and director Christopher Nolan has resisted pressure to upconvert the footage for 3D, The Avengers enters the marketplace with a commanding price advantage over it. 3-D screenings are typically a couple of dollars more expensive than standard screenings, meaning that if both films sold out every screening all weekend long (which is unlikely, but bear with us here), The Dark Knight Rises would have to open in substantially more theaters than The Avengers did just in order to catch up with it. Even assuming no sell-outs, if we were to guess that the two popular franchises would fill theaters at roughly the same rate, the math remains the same.
The Avengers, for context, had the seventh-widest opening in cinema history, meaning that only six movies have ever opened on more screens. It's unlikely there are enough open screens in the middle of the late-summer blockbuster season to accommodate a substantially wider opening for The Dark Knight Rises. The Batman sequel will likely have the widest IMAX opening of all time, and of course IMAX theaters cost more than standard tickets, too, but the numbers aren't even close. There are far more 3-D screens (about 2500) than IMAX ones (less than 600) at the most recent counts available for each.
Combine that with a longer runtime--The Dark Knight Rises appears to be clocking in at around 20 minutes longer than The Avengers. If a theater is beginning new screenings for fourteen hours, then (that's from 10 p.m. until midnight or so), then, it's likely that each screen would show The Dark Knight Rises one fewer time than it showed The Avengers last weekend. Once again, assuming that a big summer blockbuster with great reviews and a broad appeal will fill each opening-weekend screening at relatively the same level, that means that each of the thousands of screens that the film opens on would generate a few thousand dollars less income per day.
With all of that considered, it's not technically impossible for The Dark Knight Rises to break The Avengers' record and become the biggest opening weekend in the history of cinema. Technically. Realistically? It would have to perform as much better than The Avengers as The Avengers did Harry Potter and the Deathly Hallows Part 2. The chances of that seem negligible at best, and if The Dark Knight Rises were to "win" the summer it seems likely that it would have to rely on longevity to do so.