Learn English – “My hobby is to play basketball” or “My hobby is playing basketball”

We can use either the infinitive without to or the -ing form after the object of verbs such as hear, see, notice, watch. The infinitive without to often emphasises the whole action or event which someone hears or sees. The -ing form usually emphasises an action or event which is in progress or not yet completed.

• He saw her drive off with a young man in the passenger seat. (The speaker observed the whole event.)
• Maria heard him coming up the stairs towards her room, and felt scared. (The action was in progress, happening, but not completed.)

(from English Grammar Today)

Therefore, both forms are correct and have the same meaning. They might suggest different meanings when using them in past tense however.

Another thing:

After can or could with one of these verbs, we always use the -ing form, not the infinitive.

We use the present simple to talk about things that happen regularly, habitually, continually or things that are generally true

The two boys play in the park every saturday - regularly

The two boys usually play in the park - habitually

These two boys play in the village football team - continually

Boys play football - generally true

The continually and generally true usages don't work very well with play- see the link for better examples.

Compare that with are playing, which implies some continuous action that is taking place now:

There are two boys playing in the park

This means that, right now, two boys are in the park: they have been playing for a while, and it seems likely that they will continue to do so for a while.