Yes for the Trax/Thraex. He has a small curved blade that can reach around an opponent's shield, and a smaller shield.

For the Murmillo and Secutor, it's a hat competition. Secutors were usually pitted against Reitiarii - the small eyeholes in the helmet were to keep the trident, specifically, out, and the helmet had fewer features to make it harder to net.

I dig the Murmillo more, personally. The helmet has, as the Romans would say, gravitas!