I've heard it said that having Skyrim installed on a solid state drive will give it a vastly improved performance and possibly remove the stuttering. My system specs are an Intel i7 4790k cpu, R9 280x gpu and 8gb ram and I plan on using many high resolution texture packs and mods. Would installing it on the SSD over the HDD be that big of an improvement?Also would the same apply to other Beth games like Morrowind, Oblivion and Fallout New Vegas?

AFAIK, stuttering (micro-stutter?) is related to the engine and graphics driver/hardware issues. There also other issues with Skrim's memory management. None of this will be reduced by installing Skyrim to a SSD. The main thing improved by installing Skyrim to SSD is load times.

In my personal opinion I don't believe the improvements of using a SSD outweigh the costs of the hardware.

Yeah, a solid state drive won't counter deficiencies in Bethesda's game engines. For Oblivion there's an OBSE plugin to reduce the stuttering. I don't recall Morrowind being that bad but I do remember some sudden drops in fps. Skyrim can lag at times even without ENB, HD texture packs and other mods. Your hardware should be more than enough to run this game.

The next TES should run much better with a 64-bit engine and support for http://www.digitaltrends.com/computing/intel-benchmarks-directx-12-looks-faster-efficient-dx11/#!bM9woK and/or Mantle.