Personally I think that it really depends what your opponents are using.
If they have many plasma/meltaguns that can easily shoot it down, then I would take the greatsword, as it keeps it alive.
However, swooping should keep you safe from shooting attacks mostly, and shunt really does synergize well with guns, so I'd probably take the Incinerator if I were you, since you can swoop or shunt, and still fire the incinerator. -sadly my plan here has been foiled by the insidious FAQ!!!!!
Also note that the heavy incinerator really is one of the most brutal weapons for many armies. While marines may not complain that much, I'll even go so far as to say that it can ruin certain army builds that have fragile, yet expensive infantry (veteran guardsmen, eldar, tau, SM scouts, rangers) as it can simply tear apart expensive units no matter what side of the board they are on.
But also, what else is in your list? Do you have interceptors that might be able to be paired with it? That would change things definitely. (I know you say you are using Paladin heavy "Draigowing" but Draigowing isn't ALL paladins, at least most often).