Movieverse Aragorn is unlikely to become king. The movies depict Aragorn not as a confidant leader who has already been leading the fight against Sauron long before the story began and is ready to assume his destiny as king, but as a lone swordsman who has been wandering around doing nothing, and doesn't want to become king. He will likely be irrelevant in this timeline.
The movies depict Denethor as cartoonishly evil and stupid. The movies also do not depict Gondor's and Rohan's relationship, so it is unlikely Gondor will turn their attention towards defeating Saruman. His sons might be able to round up some men and assist Rohan in fighting against Saruman. Hopefully one of them succeeds dad before he thinks of fighting Rohan...
The remaining elves will no longer be tied up by the forces of Sauron. After mopping up, they could come down to help defeat Saruman, if he hasn't already been defeated.
The Haradrim and the Easterlings won't be a problem, as they will be too busy trying to secure their home territories.
Biggest change is that without Aragorn, there is no reunited kingdom. Also, the Dead Men of Dunharrow are never released from their purgatory.