For the purpose of this post, let's assume that Swiss cantons are the equivalent of American states. Given the up-and-down topography and deeply entrenched language barriers, many of the cantons could not be any more different.
Now, in the United States, each state has its own tagline. Many of them have some truth (Florida is the "Sunshine State"), but others are plain marketing speech (Idaho: "Great Potatoes. Tasty Destinations.").
But in Switzerland, cantons do not have official taglines. But this is not needed anyway as most every canton has some sort of cliché attached to it. And it is a pastime of many Swiss to delve in those stereotypes about their neighbors. Of course, this is hardly meant in a malicious way, but rather as a friendly competition.
So if the Swiss cantons did have taglines, here is what they might be:
Aargau: Carrot Country ("Rüebliland") a.k.a. "White Sock Zone" a.k.a. "That thing that connects Bern and Zürich"
Appenzell Ausserrhoden: The Original Hobbiton
Appenzell Innerrhoden: The Cowshit in the Meadows
Basel-Stadt: The Carnival Capital
Bern: Züri West
Fribourg: The Hipster Canton
Geneva: France ("C'est déjà la France!")
Grisons/Graubünden: The Real Heidiland
Jura: The Jurassic Park of Switzerland
Lucerne: The Heart of Switzerland
Neuchâtel: Where The Green Fairy was born
Schaffhausen: City by the Falls
Schwyz: Negative Taxes for All
Solothurn: Home of the Number 11
St. Gallen: The Far East
Thurgau: Cider India ("Moschtindie")
Ticino: The Sunroom of Switzerland
Uri: Crossroads between North and South
Valais: Where They Talk Funny
Vaud: Home of the World's Best Wine
Zug: Highest Income per PO Box
Zürich: Downtown Switzerland