Distance carry gain is minimal, although the 13 will roll more. Also keep in mind that a 13 is much harder to launch on the fairway. You may be limiting yourself to tee shots with it unless the ball is really sitting up. If you have any sort of a slice or fade, the 13 will exaggerate it.

I quit using a 3 wood, quite frankly, because a good hit was only 15 yards different than my 7 wood and I tended to hit it too high on a straight shot or slice it. You may fare better with a 4 wood and might even hit it lower than a 3 wood. Easier to hit on the fairway.

I just got rid of a G10 4 wood because my trusty ole Burner 7 wood smoked it on a tee shot test; however, I found another 4 wood that I can hit close to 200 and reasonably straight.

I'm about to make the change, I'm finding that I'm hitting the ball too high off the tee so when its windy i can use it. Off the deck when I make good contact it also goes too high but am very incosistent from the deck (I only hit 3 woods of deck at the range anyway)

I have a 4 wood that I can hit with a penetrating trajectory off the tee. Nike Sumo SQ. I have a tendency to airmail a 3 wood on a straight shot or hit a high fade (I chucked my Burner and R7 3W and applied the store credit toward a new Vokey SM cc 50-08).