Yes grill man, charred would be the word. That is where the outdoor cooking flavor is and you just don't get that with a gas grill. Charred and burnt are two completely different things, and I know you know that.
Now to sauce it or not to sauce it is the question. Properly BBQed meat IMO really doesn't need any sauce, none at all...….. well maybe a touch just for dipping. Just me but I think too many people think BBQ ribs has to be plastered in some bottle sauce and that just ruins it.
Look up Lindsey Kaufman's friend.... Adam Perry Lang...one of his books is Charred & Scruffed.
In it he emphasizes that if/when applying a sauce do it after you flip the piece
when it's receptive and hot
Doing it before just burns it off quickly... makes sense if you think about it.
Serious Barbecue is another of his books that offers good tips