I think there is no difference. There are some verbs that accept both conjugations, and "like" is one of them. Of course, there are permanent expressions such as "would like TO".
In British English, there can sometimes be a distinction; the gerund is used for a general statement and the infinitive can be used for a restricted statement:
I like reading. (general statement)
I like to read before I go to bed. (I don't necessarily like reading at other times)
I believe that this distinction is not made in American English.