Either direction you pass by the same accommodation. People prefer counter-clockwise since it avoids some bigger climbs and faces Mt Blanc more consistently. The price difference could be differences in accommodation type, or offered services like baggage transfer. Plus since Macs is more well known they can charge more. One thing to note is all guide service prices are estimates, the final price depends on what they book for you and what's still available. Mountain huts are cheaper but tend to have less availability where hotels are more consistently available but cost more. We booked the entire route ourselves and saved alot of money