Both are correct, although, as I understand them, they have slightly different connotations.
When we use 'constantly, forever and always + present continuous' it implies something happens too frequently and we dislike it/ it annoys us.
She is always arriving late.
Tim is constantly leaving dirty clothes on the floor.
My cat is forever licking herself.
-In all of these examples I am giving a very negative impression. Whereas, it is not always the case in the present simple.
My nephew constantly carries his toy car with him.
Carey constantly checks her emails.
In these sentences, I am emphasizing the frequency but I am not expressing annoyance.