Long ago there was only medfilt1 and no movmedian. Then there was both. Now medfilt1 calls movmedian. That fact severely limits the possibility of any significant benefits of medfilt1 over movmedian.
I don't know the answer to the question about medfilt2 in MATLAB execution. That's an image processing function, and those folks generally work pretty hard on the performance side. In particular, the Code Generation notes at the bottom of the doc page have some intriguing comments. Might be worth a try, or it might turn out that the parallelism/threading scheme only helps in 2D. Let's add the Image Processing Toolbox to the Products and see if we can get someone from that team to respond.
