I process 11x14" in trays. Why? Because I have trays. I use trays for 8x10", so the process is familiar. The idea of processing one sheet at a time in a tube and having to rinse and dry the tube after each sheet seems painfully slow to me.
I have a couple of contact printing frames for 11x14". One is a Premier, which was cheap and functional. I also have a Kodak frame with register pins and a matching punch, which is nicer, and I thought might come in handy some day if I decide to try a process that requires precise registration. If I were to buy a new one, the Fine Arts Photo Supply frames look quite nice.