Yes, most new shooters go for an AR, because they shoot a cheaper round and they are very modular and customizable, and they can be as cheap or as expensive as you want. Plus, the reality is that the vast majority of shooters, no matter how great of a shot they say they are, don't have a very good grasp of the fundamentals of marksmanship, and therefore don't have the ability to hit man-sized targets at the ranges where the AR starts to become ineffective unless they're on a frickin bench rest or something. That is to say at ranges over 300m or so. Also, a lot of people like the idea of the run-and-gun CQB stuff over more long range shooting.
Now the 7.62x51 is a Rifleman's round. With just plain old 147 grain ball, it absolutely shines where the 5.56 starts to trail off, that is from 300m on out to 800 or so, and is of course effective at closer ranges, as well. It really handles the wind better at ranges over 300, and it delivers a lot more energy and/or penetrates more "cover" once it gets there. If you have the skill to use it to it's ballistic effectiveness, you could wreak havoc on a group armed with poodle shooters or kalashnikovs by staying outside their max effective range and delivering well-placed shots at the "Rifleman's cadence" of one shot per breath.
The 5.56 AR is better for close quarters shooting, though, since it is generally lighter, shorter, and has less recoil than most 7.62 battle rifles. I guess it depends on whether you think you and your rifle are going to face primarily close quarters situations, or avoid CQB as much as humanly possible and mostly engage from longer ranges?
Personally, I like having both, as they complement each other nicely. However, my do-it-all rifle is my 7.62 M1A.
This post is geared toward a 2-way-range type situation because you asked about "assault" type rifles for real-world use, and I assume that's what you're talking about. If you want something just to plink with at the range, then you may have some different considerations.