You can truly use both as you want.
example :
il y a plein de choses que j'aime faire.
il y a beaucoup de choses que j'aime faire.
The both are totally correct !
But you have to be careful because "plein" can means "beaucoup", and in that case you can just use the one you want.
But "plein" can also means "rempli " and in that case you cannot use "beaucoup".
example :
Il parlait avec les yeux pleins de larmes.
J'ai toujours connu leur maison pleine d'amis.