Daniels? I prefer him over Carrey, actually. Daniels is primarily a dramatic actor and its rare for him to do zany comedic parts, whereas Carrey is the opposite. My favorite Jeff Daniels role is probably in the civil war saga Gettysberg and Gods & Generals where he played the real-life war hero figure of Col. Joshua Chamberlain in both movies. Shame they never made a final film in the trilogy. 
In second place was another real life historic war figure he played: George Washington in The Crossing. I only knew him from Dumb & Dumber at the time, but he did a fantastic job as Washington and really brought him to life. Best George Washington ever (sorry, Barry Botswick). 
Also liked his roles in The Purple Rose of Cairo, Arachnophobia, Speed, The Hours, and The Martian. Heard he was good in the HBO series The Newsroom (where he was the lead character) but I haven't seen it.
Carrey is probably the bigger "name" and Box Office draw by far, but Carrey's heyday was his breakout toilet humor comedies of the 90s, the last time I saw him in anything noteworthy was Kick-Ass 2 and the sequel to Dumb & Dumber, and that was about five years ago.
Ideologically, both Carrey and Daniels are hard-left loudmouths, but that's true for about 90% of Hollywood.
I think Washington was done better by the guy who played him in “Turn”!
Gettysburg & Gods & Generals are the only things I thought Daniels did well.
Carrey picked with “In Living Color”. Probably because he had good writing there.
Daniels did at least come across as sane, which apparently was also an act. His portrayal of Col. Chamberlain (and future Maine Republican Governor — the horror !) did more to introduce him to the public and elevate him as a key player at Gettysburg than at any other time.
I noted amongst autograph collectors, prior to the film, Chamberlain’s autograph could be had for a nominal price (say perhaps $50 or less). After the film with Daniels, the price skyrocketed ten times, so now you can’t get an autograph of Chamberlain for under $500.
No more need be said--