''Do you compose your music first on paper and then in a notation program?

Hi all,

After my secondary school I want to study either Classical Saxophone or Composition. 
When I am chatting with Composition professors, it seems to me that they prefer composing on paper and then they notate in a notation program.

I have tried it several times to compose on paper, but I find it really hard. Not because I don't know what the music will really sound like, but because I make so many notation mistakes. Actually, when writing music on paper, my scores look like Beethoven's (see picture) and I cannot even read in myself. . .

My question:

''Do you compose your music first on paper and then in a notation program? Or do you directly notate in a program, such as Sibelius or MuseScore?
Why?''

I think the ''Why'' is the most important part of the question.

Please let me know your opinions, experiences etc. Answering the poll would be very nice.

Kind regards,

Maarten