One would definitely say "Silkscreen of course, write your text on silkscreen". And this is roughly the purpose of the silkscreen layer. But the solder mask layer has a much higher resolution in terms of DPI and also a much higher precision in terms of alignment on the PCB. The solder mask is printed using the photographic method while the silkscreen is printed using the... silkscreening method. The silkscreening method has much lower resolution (not even close to the photographic method used for the solder mask) and also the alignment of this layer is usually poor. And this is normal - A misaligned silk screen layer by say half a millimeter will not do any harm. A misaligned solder mask on the other hand by even a tenth of a milimeter usually means "go home and do that again".
Having that said, you may now consider using the solder mask to print fine text on your boards. Here is a quick comparison video: