He's more of a singer than a dancer.
This means that the degree to which he is a singer is greater than the degree to which he is a dancer. Note the degree to which he is a singer/dancer can be expressed without comparing two different degrees as follows:
He's not much of a singer/dancer.
He's a bit/heck/hell of a singer/dancer.
This construction doesn't accept the singer/dancer for the degree should be always about an attribute, something the singer/dancer cannot express.
*He's not much of the singer/dancer.
*He's a bit/heck/hell of the singer/dancer.
Hence the ungrammatical
*He's more of the singer than the dancer.
Now, if you don't want to compare the degrees but merely want to choose one description over the other, you should leave out of:
He's more a singer than a dancer.
Which means that "He's a singer rather than a dancer" or "He's not so much a dancer as a singer".
The assassination in 1914 was more a result than a cause.
means that "The assassination in 1914 was a result rather than a cause" or "The assassination in 1914 was not so much a cause as a result".
Since this construction without of isn't comparing degrees, the can be used in some cases:
It's more the exception than the rule.