There is quite a big difference in demand between the two main types of 1921 Liberty Head gold coins. Here are the differences.
Obverse:
Type 1- Small rounded 5 with curved base at top. Date appears to be slightly punched upwards.
Type 2- Large, open centered five and flat top with date appearing centered.
Reverse:
Type 1- Liberty's hair has only several fine horizontal lines in front of her ear, while the feathers above the eagle's wing are rounded and smooth.
Type 2- Liberty's hair shows three definite ridges in front of her ear while the feathers above the wing are sharp.
Type I - 1921 Liberty High Relief Obverse
Minted quantity: just over 159,000
Value range: $10,000 to $200,000
Type II - 1921 Liberty High Relief Reverse
Minted quantity: 275,750
Value range: $5,000 to $115,000