There are no hard and fast rules about organizing a comparison/contrast paper, of course. Just be sure that your reader can easily tell what’s going on! Be aware, too, of the placement of your different points. If you are writing a comparison/contrast in service of an argument, keep in mind that the last point you make is the one you are leaving your reader with. For example, if I am trying to argue that Amante is better than Pepper’s, I should end with a contrast that leaves Amante sounding good, rather than with a point of comparison that I have to admit makes Pepper’s look better. If you’ve decided that the differences between the items you’re comparing/contrasting are most important, you’ll want to end with the differences—and vice versa, if the similarities seem most important to you.
The second way is sometimes called the block or chunk method. In this method, the writer would discuss all the aspects of the first thing and then all the aspects of the second thing. For the beach thesis, the writer would first write about the popularity, activities and scenery at Millertown's beaches and then about those same aspects at Sunnydale's beaches. The danger of this method is that the writer may end up simply describing each of the items without really drawing out the comparison and contrast. To avoid this, it's best to use language that shows comparative relationships such as "in contrast to Millertown's beaches" and "like Sunnydale's beaches."