You don't strictly need 4-bolt shoes for Speedplay pedals—most 3-bolt road shoes work with Speedplay using an adapter plate. However, 4-bolt shoes have a direct-mount pattern built specifically for Speedplay, eliminating that adapter entirely.
The big advantage is lower stack height. Without the adapter plate, your foot sits closer to the pedal axle, which can improve power transfer and give a more connected feel. You also get the full benefit of Speedplay's adjustable free float without any interference from the adapter.
Choose 4-bolt shoes if you're committed to Speedplay pedals and want the lowest, cleanest setup possible. If you think you might switch to Shimano SPD-SL or LOOK Keo down the road, stick with 3-bolt shoes and use the adapter—you'll have far more shoe options and future flexibility.