The only difference between the models you are looking at are the amount of RAM, the size and speed of the HDDs, and presence/absence of Blu-Ray. All the models have the same processor and the same video card (the hardware that really impacts longevity in playing games).
The BBK5 has only 8 GB RAM (can easily upgrade to 16 GB as there are 2 empty slots); a 1TB 5400 RPM HDD (one empty HDD bay); and no Blu-Ray.
The AS71 has 16 GB RAM (no empty slots); a 750GB 7200 RPM HDD (one empty HDD bay); and no Blu-Ray.
The DS71 has 12 GB RAM (one empty slot); two 750 GB 7200 RPM HDDs; and Blu-Ray.
So purchasing either of these three options really comes down to how much money you want to spend and whether or not Blu-Ray is a deal killer for you. One isn't really better than the other because at the BBK5 price point you can easily upgrade (Install a SSD and more RAM) for about the same price as the others. Just depends if you want to do the upgrades yourself (which are easy and there's good guides here on these forums).