Arpeggio Picking Question

[helloworld]

Hey Neil, or anyone else who can answer this question. I was just learning to play Don't Fear the Reaper from the lesson here on the site. I'm wondering if there is any benefit to using an alternating picking method instead of just down picking, or cross picking the song. I think I'm getting pretty good at the alternating picking method, but would like to know if one style is better for arpeggio than others. Thanks in advance for the replies.