It looks to me like her hair is sinking into the field, and I've learned to see that as a bad sign. But this photo on Littleton's site looks worse, so... no idea.
Here is a 1927 double eagle in MS-65, CAC that you can use for a comparison. As @jeffB said, the hair on the piece you are considering does not look sharp. That is not a positive sign. These coins have been counterfeited for many years, including coins that are made of gold, but not genuine.
We often talk her on CT about the cartoonish counterfeit Morgans and the like we see around…. Makes me sick to say this, but there are some scary good counterfeit pre-33 gold coins out there. I think you can pick up a St. Gaudens for 2k from a legit dealer. I believe I saw a bevy of them on GC last week.
Agreed the hair is too weak on the suspect piece, and I think the date is too prominent as compared to the known genuine.