Both sentences are similar, but carry slightly different meanings.
I think the most pressing thing to take note of is the difference between 見る and 見える. For a deeper understanding, I suggest checking out this thread and this thread. But, for now, I will focus on the most likely application of the word:
見る: to look. (the action of looking)
見える: to be visible. (the action of having the ability to be looked at)
私があなたを見る
If we break this down literally, it would be something like "I am look(ing) at you."
あなたが見えてます。
And if we broke this one down literally, it would be "You are visible"/"You are seen."
Thusly, if you wanted not to say "I am look(ing) at you" but instead, "I can see you" (lit: You are visible to me) it would be:
私にはあなたが見えてます。