It basically comes down to how you prefer to alternate pick. There are two ways to cross strings with AP - inside the string (where your pick travels... you guessed it, inside the string) and outside the string (where your pick goes over the string and hits it the other way around - completely counterintuitive, I know, but that's the way it goes). If you were picking one note on the B string and one on the E, hitting the B on an upstroke and going to the E with a downstroke would be inside, whereas a downstroke on the B and an upstroke on the E would be outside. Figure out which one you do more evenly/cleanly, and plan it around that - if your inside picking is better, do downstrokes for the first four notes and then upstrokes on the G, B, and D strings as you descend the arpeggio again; if your outside picking is better, do three downstrokes and then come back around on all four strings descending with an upstroke.
Note that a ton of players use arpeggios that let them hammer-on and pull-off another note (or two) on the highest and lowest string of the arpeggio - this helps a great deal with smoothing the sound out. Example:
E------------------12h17p12-------------------
B--------------13------------13----------------
G-----------14------------------14-------------
D--------14------------------------14----------
A-12h15-------------------------------15p12h15
E-----------------------------------------------... and so on
so keep that in mind if you have problems 'turning around' over one note.
Jeff