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.
Examples:
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.
For example:
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.