I always heard sliders as "faders", and pots as "rotary" boards. I think it depends if you spoke with announcers or engineers. If the current board style is sliders, then that would be my preference, though I prefer using analog boards from the late 80s and early 90s, like Harris. Although a cheaper option, I liked some Arrakis boards too. They were very simple to me.
I suppose I prefer sliders, because I have a visual layout of the levels across the board. Plus using the older slider boards felt as though I were seated at a table, ready to do my work, whereas using a rotatory/pot style board, you were up right up at it. The level meters were right in front of you. Alternately on a slider board, you'd see all of your meters at a pleasing distance. I find also that slider boards had more meters available so that in addition to left and right "program", you could have another meter to monitor a mono "sum" output.
So, +1 for sliders. 