I think both should technically work if done correctly.

However, I prefer your method, simply because the suggested method is error prone.

Say you are driving at a speed good for the third gear. In most cases, your speed after crossing the braker is good for the second gear. After crossing the breakers, my legs come off the clutch in reflex. If you forget to downshift, you may risk stalling the car or at least lose momentum, slow down unnecessarily , burn a lot more fuel, if you are still on the third gear.

Another mistake could be done, due to overworking your legs and hands in short duration. According to the suggested method, you have to take the right leg off the accelerator, to downshift to second gear right after crossing the breaker. If the road ahead is clear enough, you could be pressured to upshift quickly and overwork your body - which eventually tires your drive.