thunderbreak-san,
There is no difference between the two.
The only thing you have to be careful of is the wording of what comes before it (when you include what you are studying). For example...
日本語の勉強をする
日本語を勉強する
If you're going to use 勉強をする, then when you specify what kind of 勉強 you are doing, you need to use の: 「日本語の勉強...」
If you're going to use 勉強する, then you use the object marking particle を to specify what kind of 勉強: 「日本語を...」
So basically, you can't have two を in a row:
× 日本語を勉強をする
I hope that helps!