The third alternative (and best IMO) is to buy a PC case with lots of drive slots and transfer everything into it. With a NAS you’re going to pay a ton of money for the NAS itself which is just laptop-equivalent hardware and a fixed number of drive bays meaning you can’t expand it when it fills up without buying more expensive hardware, and you’ll also be forced into buying matched drives. With an HDD enclosure, you’re spending less money but again fixed on the number of drives while also being somewhat unreliable due to the USB connection.

I use a Fractal Design Define 6 midtower case which can hold around 12 HDDs. For hardware I bought a mobo with the most SATA ports I could get and began slowly buying drives as my storage pool filled up, eventually needing an LSI HBA card to expand the number of SATA connections. This is the best value IMO as the cost is comparable to buying a NAS, you can add drives as you go with a much higher drive capacity, the connection is rock solid, and you can run real PC hardware.