SSD's make a huge difference in playing back large templates because they allow you to use much pre-load buffer sizes in Kontakt (streaming from disk instead of loading everything into RAM). The key parameter is the random seek time - SSD's are far faster than HDD's there. The sequential read times that everyone quotes are less important for sample playback because you are reading a large number of individually small samples, a much different scenario than working with multi GB HD video files that tend to be primarily sequential reads. Especially if you are using any EWQL libraries since PLAY is very unoptimized for read performance.
32GB on a LGA 1155 (Sandy/Ivy Bridge) or LGA 1150 (Haswell) based system (which max out at 32 GB) goes a very long way with SSD's. Once you have worked with an SSD based sample playback system, you will never want to go back to HDD's. The Crucial M500 and Samsung 840 disks are pretty reasonable these days. You can get a 250 GB Samsung 840 for $175 from Amazon. There is a lot of discussion on the web about the write longevity of the TLC Samsung 840, but in a sample drive that is 99% reads, it is absolutely no problem.
FYI, the i7-3770 is an Ivy Bridge CPU, the i7-4770 is Haswell (Intel's latest generation). One advantage of Haswell is that the chipset supports 6 SATA III ports as opposed to SB/IB which supports only 2 SATA III ports and 4 SATA II ports.