^^ Honestly I used to rock sz 9 M lunargrands but now have gone wide and sized down another half size. Basically I wear 9.5 in everything that is TTS (i.e. Jordan 1s, AM90s, Asics GL3s (tight)), but when I got my first lunargrand, I quickly found out that they run big so I half sized down and ended up with a 9 M. Although they fit fine with some tightness in the front, I always thought that they were a bit on the long size. I then decided to try on an 8.5 M which fit like a glove length wise, but super squished in width all over (mid section and front). I took a leap of faith and ordered an 8.5 W and never looked back.
To me, the W is noticeably wider. Meaning, if the M is squished in the mid section and front, you will hardly touch the sidewalls of the W with typical lacing, but not enough to feel like you are wearing clown shoes or something. If the M is only squished in the front, the W may be too wide for you. Overall though, it is definitely wider. I guess you could always tighten the laces more if you wanted.
Hopefully that helps.... I would honestly just put in an online order for a W shoe and give it a shot. If the fit isn't right, just return it. You may also want to visit a store to half size down on a M to see if it fits length wise and use that as a starting point. I think stores don't typically sell W models, but great for trying on an M.