It's important to both 1) understand the history of pizza in the United States, and 2) know what is meant by "East Coast" and "West Coast" pizza to answer this question properly.
The pizza we're largely familiar with in the United States is Pizza Napolitano (from Naples). This is the thin crust pizza, often served as a pizza margarita (after Queen Margherita), with the three colors of the Italian flag (red tomato sauce, green basil, and white mozzarella). Pizza Napolitano came to the United States with Italian immigrants in the late 19th to early 20th century.
East Coast pizza is generally typified by pizza from New York and New Haven, both homes to large Italian immigrant communities. New York pizza tends to be extremely thin; New Haven pizza can range from thin (Sally's Apizza) to chewier (Frank Pepe's, opened in 1925), but both tend to be charred on the crust. East Coast pizza has historically tended to be more traditional in terms of what is put on top of it: sauce, cheese, sausage, pepperoni, other meats, and vegetables.
What we generally refer to as "West Coast" pizza is a more modern creation, and results from the combination of pizza with California cuisine: a chef at Wolfgang Puck's restaurant Spago was credited with creating California pizza before leaving to start California Pizza Kitchen, where the style was popularized. Toppings play a larger role in California pizza and tend to be less conventional than on the East Coast (you would never find arugula or bbq chicken on a true New York slice), and historically, less attention has been paid to the crust.
So when we say that East Coast pizza is better than West Coast pizza (I say this as someone who spent 4 years in New Haven, and has spent the last 2 years in San Francisco going to every pizza place in the city), we might mean that it is more authentic to the archetypal America pizza, New York/New Haven, which long pre-dates California.
It's worth noting, however, that in the past few years, there's been a movement that stresses authenticity of ingredients. This means that far more care is being put into crust and sauce (type 00 flour, artisanal wood-fired ovens, San Marzano tomatoes), as well as fresh and inventive toppings–and this is happening on both coasts (cf., Lucali and Di Faro in New York; Pizzeria Delfina and Tony's Pizza Napolitano, in San Francisco).