I’ve searched but couldn’t find an answer. It doesn’t seem to be age or size, as up to the largest spiral galaxy, they differ widely from what I’ve seen. There is even a weird galaxy where its stars rotate in a circle around its center, not extending inward or outward.
Maybe composition or rotational speed? If that is it, what is known about it in more detail?
The models of galaxy formation are too incomplete to give good answers to this question. Factors such as matter density, dark matter density, angular momentum and historic interactions probably all play a part.
The best current model is the Density Wave theory - the galaxy is a rotating disk of stars in elliptical orbits, and these orbits align to produce areas of density (the spiral arms). Stars move in and out of the arms as they orbit the centre. The density waves themselves may contribute to new star formation. I guessing that the higher the eccentricity of the elliptical orbits, the tighter the arms. Close encounters with other galaxies will trigger new elliptical orbits that may form additional density waves (more apparent arms).
If the orbits have little or no eccentricity, the galaxy could be a flat disk with no arms at all.
The people who study these things seem to devote a lot of effort to observing other galaxies, but how much exactitude is there to their mapping of our own galaxy? Are they pointing outwards because there’s not much more to learn by observing our own?
Other galaxies have the obvious advantage that you can see the whole structure of them and see comparable galaxies from many different angles. Our view of our own galaxy is from a not-very-informative position, at least so far as overall structure is concerned. You can still make inferences with careful mapping, but it’s harder. It only became relatively recently known, for example, that our galaxy is a barred spiral, as opposed to a straight one.
Besides, there is only one “Our Galaxy” but lots of others, so just by numbers you’d expect more time to be spent on them.