Banjo bolts use two ,usually copper, washers to seal the brake fitting onto a flat machined seat on the outside of the caliper casting. The other type of fitting has the brake tube/hose flare seating on an angled machine surface inside the inlet hole of the caliper. It would be pretty much impossible to go from a banjo type inlet to a flared tube/hose type. Going the other way would be easier, but would still require some machine work on the calipers.
We rebuild calipers here at work, and the banjo style is used as much as the interior seat style. As Andy mentioned, one type has no particular advantage over the other.