NO. The manga ended so much better than the anime.
But, yes, both anime and manga Light freaks out because he doesn't want to die, but in the manga, he freaks out even more when Ryuk writes his name down.
He dies within the same warehouse, never runs outside or anything.
And Mikami never stabs himself, he was just taken away to the police. He even betrayed Light, saying that hes no God.
Light dies more realistically in the manga. Instead of beautiful sad death, Light actually looks like hes having a heart attack, then he dies with the scariest expression.
I personally like the manga ending better than the anime because in the anime, you feel sorry for him when your not suppose to.
And heres a dead scary Light.
http://i3.tinypic.com/71wxfg7.png