Games don't shutter/stutter due to a hard drive. Data is copied into the System or Video RAM and runs from there not directly from the hard drive which is the reason there USED to be issues.
There have been issues in the past, but not with modern games. I have specifically tested 200+ games to see how they compare on a good SSD compared to a Hard Drive.
The SSD loads games on average about 2x faster. That's nice for SKYRIM type games especially which have MAPS or BUILDINGS that require frequent loading.
*Another issue is that that hard drives become SLOWER as they fill up (mechanical rotation). If you access the data at the 2TB point on a 2TB drive it's slower than a comparable 3TB at the same point.
**My advice is get something like a Seagate 3TB 7200RPM drive that costs about $110 USD, and perhaps a 120GB Samsung 840 EVO for your Windows drive (games/Steam on the hard drive).
Other:
1) In WITCHER 1, I was convinced the stuttering was slow texture loading due to the hard drive. It turns out it was an issue with HYPERTHREADING. I disabled HT for the CPU and the game ran smooth.
2) Diablo 3 had some weird issue that apparently worked better on an SSD but it should have been fixed long ago (I run on an SSD).
3) One or more of the Assassin's Creed games worked SLIGHTLY better on an SSD due to textures loading but you really had to sprint on the HORSE to notice.
4) SSHD:
Only get one for your MAIN DRIVE to speed up Windows.
**At $200, the best value overall is:
a) $90 Samsung 840 EVO (120GB) for main Windows/Apps, and
b) 2TB/3GB Hard Drive for games/steam/backups/downloads etc.