It will be a little richer. And as an added benefit, it will stay "fresh" tasting for longer by not drying out quite as quickly so enjoy the cake on the day and enjoy that leftover slice the next day just as much.

My recipie for muffins (which is essentially a basic white cake mix with flaviourings of choice added) has a range rather than a specific quantity of fats (oil or melted butter) to add. Add a little for a lighter muffin, but tastes best straight from the oven. Add more for muffins that you want to taste as good as fresh baked even the next day.