Thanks to your post I've also spent an unreasonable amount of time considering this today. I think... I
think... a flyover is for everyone, we look up and say "wow!" and feel the bolstering effect of our tax pounds/dollars/pfennigs in the sky above is. When the RAF fly over the balcony* the people are sharing the experience as much as the honking toffs on the balcony. It's for all of us.
A parade of heavy, armed military vehicles is directed much more at the statesperson in the main seat, everything is visibly arranged for their approval with everybody else just spectating - it's not for all of us, it's for
us to watch
them with
their massive arsenal.
*The point at which I always shout "bombs away!". True story