GitS and Eden of the East have very little in common. The only major element shared between the 2 series (I assume you mean GitS:SAC) is the mystery elements during the Laughing Man case, and that is largely left to one side during 1st Gig.
The product description on amazon should be enough to see whether you'd be interested (minor spoilers for eps 1 & 2) :
"On November 22nd, 2010, ten missiles strike Japan. Known as Careless Monday, this attack does not result in any apparent victims, and is soon forgotten by almost everyone. Then, three months later... Saki Morimi, a young woman currently Washington D.C. on her graduation trip, is saved by a mysterious man, who has lost his memory, and has nothing except for a gun and a phone with 8.2 BILLION yen in digital cash."
If the description makes it sound interesting you'll probably at least enjoy it. Just be warned that the series only wraps up some of the plot threads, you'll need to watch the 2 films to finish the story.