The first example uses a present active participle (in essence an adjective describing Jameson). Many would like to see a comma before 'outscoring', but there is leniency on this.
The second uses a gerund (a type of noun formed from a verb). It is linked to Jameson with the preposition 'by'.
I must have a blind spot to this because, no matter how long and hard I look at it, a line such as: "Jameson won the title outscoring Jeffries on a unanimous decision", reads to me. I wish I could understand why it doesn't.