Only issues I know of are that the BTUs are not as high but not anything you will really notice.
Now however if I forget to turn off a LP grill the worst that happens is that it burns until I run out of propane.. I wouldnt want to do the same with NG.
ETA I think you were looking at a Weber grill those come NG or LP so I believe the burners are taylored to the setup. Its a better setup than the LP grills with a converter as far as getting up in temp from what I have been told.
This post was edited on 10/1 at 3:37 pm