HardOCP conducted a test to investigate the real world gaming performance of HDDs and SSDs, you can read the article over here. The site concludes that the prime difference between both technologies are the faster loading times you get with a SSD, in terms of actual gameplay the tester didn't notice any difference:
In terms of raw video game performance our conclusion is that upgrading to an SSD made absolutely no difference in gameplay performance. Honestly, we did not expect that it would, hence why we held back for so long on upgrading to SSDs. In every game we tested the performance fell within the margin of error for a realworld gameplay run-through. We tested some very demanding games as well such as Battlefield 4 and ARMA 3. However, no game showed any performance advantage with the SSD versus the HDD. The framerates were the same, the frame consistency was the same.
Here is what was better with the SSD, as you might guess; load times. Loading each game was significantly faster on the SSD. Transitioning maps during gameplay was also significantly faster on the SSD. Loading times were improved, and we had a better experience overall simply because game data loaded faster.