Hello there! I'd like to contribute a little bit although I haven't reached that level in Japanese so far (I can speak relatively fluent Chinese though, so this might maybe help a bit to understand more thoroughly the meaning of the kanji).
According to Japanese dictionaries, both words have the meaning of "management" behind them. My guess is that 管理 is however very often used as either a noun or a verb whereas 経営 is more used as a verb (although it could be a noun too). In Chinese, the true difference would lie here: 管理= management 経営= operation. You manage and operate. Usually those who run a company also own it, hence Yuki's answer.
I can of course be wrong, but this is how I see things based on my Chinese knowledge
Hope this might help!
Ed
