Im gonna start off by saying that yes, the sword jump method is faster. However, the method is very unreliable unless you've practiced it for hours. If youre just a casual player, youll waste more time trying to get the sword jump than if you were to do the fight normally and break the armor.

So the method I recommend is break the armor normally. The killer of this fight is the sigil on Gaius' arm. The amount of shaking and stamina drain on this sigil can be brutal. With that being said, the order of the sigils that you destroy can make the fight a little easier.

Start with the normal way, break the armor, run up the sword and climb up to the head. Once you take the head sigil out, make your way down to the stomach. The stomach sigil is the easiest one to take out, and even better, there is a very stable ledge around his belt-line that you can use to regain all of your lost stamina so you can start with a full amount before taking out the sigil on the arm. Stand on the left side of Gaius on his ledge around the belt line, and line up the jump from the stomach to the left arm. You should be able to land almost exactly on the sigil requiring very little adjustment, thus saving you a little more stamina. With a full stamina meter, it should be a bit easier to try and take out the arm. I spent way more time than I would have liked on this fight, trying different methods, and this one was the one that was most successful.

TLDR: Break armor > Take out head sigil > drop to belly > take out belly sigil > regain stamina > jump from belly to left arm > take out arm sigil.