The biggest reason for using Montezuma over Atahualpa, in my opinion, is that Montezuma is responsive, meaning that a Montezuma site will reconfigure itself so it looks good on different viewport sizes, like tablets and cell phones. More and more users are browsing the web on mobile devices, especially the younger, more affluent crowd, so it makes sense to make your site responsive, especially if that is your target demographic.
Montezuma also gives you a lot of flexibility in designing your site. You can easily add as many sidebars or widget areas as you'd like, for example. Take a look at all of the sites in the
showing off thread and you'll get an idea as to how customizable the theme is. While many of the sites don't deviate too much from the basic appearance of the theme, others look so different that it's difficult to tell that Montezuma was used in the design.
As far as what Montezuma
can't do that Atahualpa can, the only thing that I can think of is Atahualpa's rotating header image, and that can be done using a carousel plugin in a header widget area. I've converted a couple of sites from Atahualpa to Montezuma and was able to re-create the appearance and functionality very closely. The hardest part, if you are used to all of Atahualpa's options, is learning a very different way of making changes to your site. It parallels closely with the way themes are written, so it will be big a help if you have a decent knowledge of HTML and CSS.