I wouldn't necessarily buy a new board for better contrast if you're considering only those two woods. The walnut and mahogany aren't that far apart in the spectrum. On the walnut/maple hardwood board I have, sheesham looks just fine, as does the walnut from the more expensive set I have. If you want more contrast, perhaps try padauk or ebony and maple for the board?
Sheesham pieces on walnut or mahogany for better contrast?


Don't spend too much time on a board you aren't able to see. Actually I recommend you buy one of each colors you prefer of plastic boards then change them if you get bored with the color. ALso you are asking what color board is better. But it is very subjective. How could anyone tell you for sure?
Personally I found that if I play on a wooden board then pieces that are full black and full "blond" are best for contrast. If I have pieces at home which are brown finish wood pieces and "blond" then they actually look the best on one of the cheap roll up green square boards. IMO brown color and green go well together.
I own the Dubrovnik 2.0 Sheesham pieces from Chessbazaar. I currently own a cheapish walnut and maple chessboard. Sometimes I have the feeling the contrast isn't enough since it's both brown.
When I look at the house of staunton mahogany and maple boards, the mahogany looks reddish, wich I think gives a better contrast? Then again, pictures can be misleading.
https://www.houseofstaunton.com/mahogany-and-maple-wooden-tournament-chessboard.html
Would it go well with Sheesham pieces?
What is your experience/advice?