I've used the mesquite or hickory a few times for grilling...it's OK, but not the same as using a chunk or two of your favorite smoke wood. Never tried it to fire a smoker, as I felt it could result in a heavy flavor. As alblancher and SmokinAl mentioned, for the best results, it's better to be in control of the amount and type(s) of smoke you're using.
BTW, if you've never blended any smoke woods, such as pecan/apple, pecan/cherry, hickory/pecan, or triple blends, you should give it a try. Use a sweeter, milder wood along with something stronger/sharper for a smoother flavor and aroma. I've used this method for a couple years with most of my larger cuts of meats, poultry, sausage loafs, steaks, chops and ribs.
Eric