More of a/an/the something than something
Solution 1:
When describing something or somebody, only the indefinite article can be used:
He is more of a scientist than a physician. (This means that he can be better described as a scientist than as a physician.)
The final was more of a battle than a game. (This means that the final could be more accurately described as a battle than as a game.)
The example provided by Jim in a comment does not reflect this structure, since use is being made of the verb pattern "see something of something" (the first "something" is "more", meaning "more things"):
- We saw more of the ocean than the island.
Similarly, we could have this sentence:
- We heard more of the story than the real facts.
In both cases above, "more" means "more things" and is not used for description. In conclusion, if you want to describe by comparing using "more of", use "a/n", not "the".
Solution 2:
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".
Similarly:
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.