Gel stain, yes; Polyshades, no. Gel stains work very well on pine because they don't penetrate much and thus avoid blotching (uneven absorption of color due to uneven cellular structure.) Polyshades is a varnish with a lot of pigment. Sort of a halfway point between varnish and paint. It is very difficult to get it on evenly and without streaking.

Realize that the pine will never match the oak as they are radically different grain structures. The best you can hope for is a similar color.