If you're upgrading your PlayStation 4 with a new hard drive, you're likely deciding between a larger regular drive and a faster but smaller SSD. Digital Foundry has a side-by-side comparison of the load time performances between several different hard drive models, and the speed difference is substantial.
The 240GB SSD regularly handled loading times at up to 10 second faster than its hybrid and standard cousins. Of course, that speed comes at the cost of storage, as the other three hard drives could all hold a minimum of 1TB in data, including a very affordable 2TB drive that inspired this comparison in the first place.
Digital Foundry also compared game performance between the four drives, and found that the SSD also came out ahead, but only minimally.
Ultimately it comes down to what you value as a gamer. If you're hungry for the fastest performance possible, an SSD will give you that. But if you need the extra space, the 2TB HD that Digital Foundry recommends will give you some significant bang for your buck.
You can read their full report on the cheap 2TB hard drive here.