i have the same dream as you还是i have the same dream with you .

应该是
I have the same dream as yours. 我和你做同样的梦。

as 表示“一样”的意思
with 是“和...一起“

如果想说“我和你一起做梦”，应该是
I dream with you.

是 I have the same dream as you.
当表示“和...一样”时，the same ＋名词＋as，这是固定搭配，介词就用as，所以在这句话里，主要不是as和with的用法或意思的区别，而是固定搭配问题

i have the same dream as you

首先请你看一句话: Linda isn't as tall as Jenny. 这句话换个方式也可以这样说:
Linda isn't the same height as Jenny. 现在我们用这两种说法把珍妮和琳达两个
姐妹作个比较. 在下面这组练习里有几个字你可能不太熟, 比方 "女用手提包"
purse 和 "女衬衫" blouse. 这些字等一会儿我们还会重复练习. 现在我们开始
作语法练习. 请你注意听.
M: Linda isn't as tall as Jenny.
F: Linda isn't the same height as Jenny.
M: Linda isn't as old as Jenny.
F: Linda isn't the same age as Jenny.
M: Linda's swimming suit isn't as expensive as Jenny's.
F: Linda's swimming suit isn't the same price as Jenny's.
M: Linda's hair isn't as brown as Jenny's.
F: Linda's hair