Because Lumia's battery scores better than 820's. And we all know that every nook and corner has a Nokia Priority showroom and they will take care of the battery. No one should risk opening a uni-body phone by themselves.
You can go ahead and easily find an 820 for about 20K. But according to the usage, I don't think your mom will make the most out of 820. That being said, there's a chance that Lumia 820 will get more updates that 720 in future because higher specs. And if you want to play games once in a while, 820 will be a better buy.