Jennifer, either one would work, but I think carriage bolts would be the better choice. Easier, too, since you'd want to do lags from both sides. Spacing; I would zig-zag the bolts 2" from the top and bottom of the joist on 14" to 16" centers. I'd also use a construction adhesive between the layers.
Another really good trick in beefing up support when sistering a joist is to put a layer of sheet metal in between the original joist and the new joist, then screw the pair together.