Each different badge type has different badge art on it, and you can choose your favorite one. The types are either classic anime archetypes or genres, like Mecha, Ninja, and Really Angry Woman, or references to specific, well-known characters, like Ballerina Duck (Princess Tutu) and Silhouette With Glasses and Smile (Dr. Tomoe, Sailor Moon S).
The difference between regular and premium is noted on the badge by the presence of your name in Japanese under the English version. It gets you advance seating in big events like the concert, at-con discounts, and other at-con perks.
And all this information can be found here:
http://animepunch.org/pages/info.php