The most significant indicator of the "size" of the coil is its surface area. Thicker wire has more surface area, but so does a longer wire (more wraps or wrapped on larger diameter). Almost exactly the same coil size can be made with either wire and in that case will produce the same vape except for more subtle differences. If a difference of surface area results, that will have a bigger effect than any secondary difference.
Older battery units were unadjustable so there still lingers in
vaping an obsession with coil resistance (often it is a generally true that lower ohm
coils are for higher power, but not necessarily). One had to not only end up with the right size coil, but the right resistance to draw the right amount of power for that coil, so the size of the wire had to be proportional to the size of the vape. With variable
devices there is some limit to resistances but otherwise it doesn't matter.