The spell cloudkill creates a "20-foot-radius sphere" and wind wall creates a wall "50 feet long, 15 feet high, and 1 foot thick".
So, each spell does exactly what they say it says it does.
If the Cloudkill were cast in front of the Wind Wall, it would be kept at bay, or, would it be dispersed as stated in Cloudkill?
This is how I would as a DM, with the information above. I would just as happy with a DM ruling the other way because this is an interesting edge case.
The strong wind from wind wall isn't acting like a normal wind, it isn't just blowing everything everywhere in the direction of the wind. So, it wouldn't blow the whole cloud away, but it would separate the cloud where it was cast. The sizes of these things matter. The wind wall would cut the cloud with a 1 foot line from top to bottom (assuming both were cast on the ground).
If the Wind Wall were cast down the center of an existing Cloudkill Would it be dispersed only in the area of the Wall? Or would the entire cloud be dispersed?
I personally would rule that the ony the 1 foot path would be carved out, as stated above, for the reasons stated above.