Why would anyone get a 6-1/2" over a 7-1/4" circular saw? Is there something a 6-1/2" can do that a 7-1/4" cannot?
The 6-1/2" circular saw is great for working due to its smaller size and weight over the larger saw. But you are limited to depth of cut that can be achieved. For example some saws this size will not cut all the way through a 1.5" thick lumber with the blade angled at 45 degrees. The lighter saw can be a real benefit for jobs such as cutting sheet goods on a roof job.
The 7-1/4" saw will support a deeper cut which is particularly useful when making certain types of cuts. For example the Dewalt DW364 saw is capable of a cut depth of 2-7/16" when set with the blade in the normal 90 degree position. At a 45 degree angle this saw can cut 1-7/8" deep which is needed when cutting things like rafters that require cutting though conventional 1-1/2" thick framing lumber.
The main advantage of the smaller saws was that the smaller blade required less torque to drive, letting them run on smaller motors and stretching the battery life. The weight reduction is an incidental outcome.
In other words, full-size is better, all things being equal -- but all things may not be equal.
The 6 1/2 is great for sheet goods. I bought a 20V version and it's great for cutting plywood. With the smaller saw & lack of electrical cord I'm able to cut a straighter line than with my 7 1/4 saw. I own a power miter saw for cutting 2x4's so i found that depth of cut hasn'tbeen an issue for me.