Enzo_86, comparing an I5-4440 and the I5-4440s, graphics wise the performance will be same since both processors have HD4600 with a base frequency of 350 MHz. If the motherboard comes with a feature that dynamically increased the graphics engine speed it may go up to 1.1 GHz, in other words both CPUs perform the same on graphics.
The only difference is going to be the TDP and the clock speed. http://ark.intel.com/compare/75038,75040
BTW, I’m only comparing these 2 processors since the I3 processor model number was not included on your post.
Thanks for your reply sylvia and sorry for the wrong title, which should obviously read 4440 vs 4440s... coming back to the matter of TDP. From your reply the slightly lower base CPU freq. seems like the only limitation the lower TDP on 4440s creates, so can I safely assume that apart from that the 's' version is no worse for even heavy duty tasks like games and other apps, despite the lower TDP cap?