From a practical point of view, the standard 3x3 arrangement is far easier to restring and easier to build. The slotted headstock has a more vintage look to it and is supposed to give a better string to neck 'contact' (presumably because the string post is held at both ends).

Presumably the 'classical style' no-name tuners had thinner metal rather than thicker plastic posts? I'd imagine even plastic posts themselves would last a decent amount of time with metal strings, but the main difference will be in tuner accuracy. Even if both tuner types had the same gear ratio, say 14:1, the larger diameter of the plastic posts would make it a lot harder to tune accurately.

Say the metal posts are 4mm and the plastic 8mm in diameter. As circumference is pi x diameter, the plastic posts would have double the circumference of the metal posts and so would wind on twice the amount of string per turn than the metal posts. So whilst the gearing of the tuners might be the same, and is high enough to stop the post moving under tension, the plastic posts would make it feel like a 7:1 ratio in terms of being able to move the string a small amount and not keep over or undershooting the correct pitch when tuning up. Fine on nylon strings that stretch a lot and need a lot of movement, but not good with steel strings.