I don't remember which I killed first, though Ornstein (and I assume super Ornstein) is weak to fire and you should have some pretty hefty pyromancies and fully upgraded glove in NG+. In either case, (Great) Combustion is good for the fight, it has a short range but is decently powerful and a VERY quick cast.
You can further boost the damage by swapping in a bellowing dragon ring which you can buy from griggs and the dusk crown helm (which I think you can access before killing them). The Dusk crown boosts casting damage, but increases magical damage to you, but since Farley and Spade don't use magic it shouldn't be an issue.
The Power Within pyromancy which boosts all damage (including weapon damage) +50% for 100 seconds, but causes constant damage will also help you win the race. Since Smough is slower you should have no trouble being able to occasionally top of your HP if Solaire is keeping Ornstein busy.
Though Smough is stronger against fire, with the spell buffing I would expect you to be able to still outdamage the Sunbro. Then once you've used pyromancy to win the race you can use your remaining charges and the chaos sword to chip away at Super Ornstein.
You are going to have a really hard time killing Smough first solo since Ornstein is so quick.