If you’re crosspicking then I don’t think it will make a difference on the technical front however musically you might find you have a natural preference for one or the other depending on the part you’re playing,
In 8th/16th/32nd note sections I like to play downstrokes on downbeats because it generally feels more musical to me. I’m currently trying to learn Andy Wood’s “ShrednecK” (albeit no where near his speed) and the intro has a sequence of rolls that mix 8th and 16th notes and while most of it is cross-picking there are cases where it feels more natural to hit two down strokes in succession where they fall on the 8th notes and kind of almost “air-stroke” the in between upstrokes to maintain the 16th note feel. For me that gives a more musically rhythmical feel to the picking.
On the other hand a succession of triplet rolls feels more natural for me to go with a strict alternative approach but that means the start of each triplet alternatives between down and up strokes