Which one is correct?
- メガネをかけると見えます。
- メガネをかけると見られます。
The first one is most likely the one you want. Here is how to think about the difference between the two:
見える is used when the scene naturally enters your eyes, describing your ability to see.
I can see with glasses on. メガネをかけると見えます。
It's a clear day so I can see far off into the distance. 晴れているので遠くが見えます。
These letters are too small for me to see clearly. 文字が小さくてよく見えません。
見られる is used to show potential based on some condition.
It can sometimes be a difficult distinction to make when thinking about it in terms of English. In my experience the former is much more common than the latter.
Note that 聞こえる vs 聞ける is a similar case.
Both sentences are correct, but 見えます is more common.
見られます sounds a bit awkward to me, because the passive form of 見ます is also 見られます. ('to be seen' rather than 'can see')
You may also find people use 見れます ('見られます' without ら), which is often called ら抜き言葉 (ra-removed word). This is nonstandard and colloquial, and I personally avoid it whenever possible, but many people use this very often.