Well the main difference in the two is with the writing and the symbols they use. the communist government after taking power wanted to bring literacy rates for the nation up but ran into the problem that the traditional symbols where very complicated making it difficult to learn. their solution was to make the symbols easier to write and read so they invented the simplified system.

for example:

Open

Traditional - 闡

Simplified- 开

See how much easier it would be to learn to write in the simplified version.

you may want to try /r/asklinguistics as well.