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Way back in the day when I was first learning Japanese, I learned that you
could add `ことができる` to a verb to indicate potential. Like so:

> 食{た}べることができる
>
> _(I) can eat (something)_

It became my habitual way of expressing possibilities.

Then later, I learned that you could just modify the verb and get the same
thing:

> 食{た}べられる
>
> _(I) can eat (something)_

I know that this is also the passive voice, but, unless I'm mistaken, it can
be used strictly as a way of expressing potential.

I still tend to habitually say `ことができる`, though. It tends to jump out of my
mouth before I realize that I could have probably modified the verb. I think
because my brain thinks they are the same thing, so I just go with the usual.

So... are they different?
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grammar verbs potential-form
ことができる versus V~える form
I think `～ことができる` has more to do with the potentiality (real word?) of things
out of your control and `～（ら）れる` has more to do with your abilities or things
you can control.

>   * 雨が止んだら、テニスにいくことができるよ！ → After the rain stops, we'll be able to go play
> tennis (can't control the rain).
>   * こつこつ日本語勉強するなら、難しい漢字も読めるようになる。 → If you keep up with your Japanese
> studies, you'll be able to read even difficult kanji. (can control this)
>

Of course, this is a slight nuance, and I think the two forms overlap a great
amount.
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I'm not entirely sure, but ことができる I think is more 固い表現 than using the
potential verb. And is usually taught before the potential form because
grammatically structures are easier for students to pick up.

here is a forum with the same exact question btw

<http://forum.wordreference.com/showthread.php?t=135581>
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Very simply :

  * 食べることができる

I am technically able to eat. I have a mouth, a stomach, and so on. When you
ask "can you do this for me" and your witty friend replies "yes, I can" but
doesn't do it, that's this meaning of potentiality that he chose to
understand. You'd use this form to say "I cannot time travel" or "I cannot
fly". You cannot do anything about it, you're not responsible (which is a very
Japanese way to say things).

  * 食べられる

I can eat, in the other meanings :)

For example, "I can't go with you because I have some work to finish".
Technically, you can go, but for some reason, you must abstain from going. You
can do something about it, you're responsible for not going/doing.
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I'm a native speaker. The expressions of ことができる and ～られる are almost the same
meaning. Don't think so difficult. You can use the expression you prefer.

Examples:

> 雨が止んだら、テニスに行くことができるよ！  
>  雨が止んだら、テニスに行けるよ！  
>

They have the same meaning. Both of them are used in daily life conversations.
There is not the difference between the two sentences in my linguistic sense.  
ことができる does not depend on in particular saying about the technical potential
or saying something in the context about uncontrollable things.

> こつこつ日本語勉強するなら、難しい漢字も読めるようになるよ。  
>  こつこつ日本語勉強するなら、難しい漢字も読むことができるようになるよ。  
>

The same meaning !!

> これが終われば、寝られるよ。  
>  これが終われば、寝ることができるよ。  
>  You finish this, then you may go to bed.  
>

Those sentences are also in the same meaning.  
And furthermore, in the linguistic sense, ことができる and られる don't have any
differences whether being polite or impolite. Both of them are used in
conversations of family, friends, lover, business situations, polite
situations, and so on.

When I want to emphasize the potential or capability in the context, I tend to
use ことができる. But they basically have the same meaning.
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