birkenstocks would be mostly biodegradable. the leather, the cork, the buckles etc. i don't know what the sole is made of, but i know you can get them resoled- i had a pair that i wore almost daily that lasted 10 years.
crocs i believe are made of some sort of vinyl or plastic- they would not be biodegradable unless they were made of a natural rubber material. i have no personal experience with them, so i don't know exactly what they are made of, but i thought i would point out that birks are fairly earth friendly. and you can get them in birkoflor- a recycled material that does not require killing animals.