In the Old West - the .44-40 Colt Single Action Army was called the 'Frontier Six-Shooter', while the .45 Colt was called the 'Peacemaker' in general parlance.
As a matter of fact 'all' .44's were referred to as 'Frontier' revolvers.
That said - the .45 Colt round is a straight case, while the .44-40 has a tapered case.
That's harder to reload - from the reloader's point of view - but great when chambered in a carbine or rifle, as they feed smoothly, thanks to the construction of the round.
Of the two - it's really up to you.
For better accuracy - the .44 Special has long been touted as being exceptionally accurate and was a favorite of Elmer Keith.
Good Luck,
Scouts Out!