Gandolfini hands down. Tony’s only bad when he has to be. Jack is a creep sunup to sundown.
Who would play a better Orson Welles, Gandolfini or Drew Carey? 
Gandolfini in a heartbeat. Carey doesn’t have the acting chops.
Who is less like his best-known character, James Gandolfini or Leonard Nimoy?
Nimoy, I suspect. Evidence would lie in that lame “Believe it or else” schlock he did back in the 70’s. Gandolfini at least has some bouncer experience.
Whose contributions to popular music are more annoying, Nimoy’s or Shatner’s?
I’d say Nimoy’s, which are just painful. Shatner’s Lucy in the Sky With Diamonds is so bad it’s funny.
Who played a detective better, Shatner or Buddy Ebsen?
Buddy Ebsen.
Who would have made a better Tin Man, Ebsen or Clark Gable?
Nimoy. Bill’s decided to have fun with his lack of talent, and it makes him a lot of fun to listen to.
Who’s done a worse job of trying to separate themselves from their most famous role, Nimoy or Tina Louise?
Ebsen. He and his sister were distinguished dancers in the early 1930’s.
Whose effort at a television comeback as a TV detective is more watchable in retrospect: Buddy Ebsen, or Dick Van Dyke?
Van Dyke
Who was a better physical comedian: Dick Van Dyke or John Ritter?
Van Dyke, although it’s a closer call than you might think.
Who had a more wretched “English” accent, Dick Van Dyke or Kevin Costner?
Costner, at least to my American ears.
Whose Baseball movie(s) are more believable, Costner’s or Tommy Lee Jones’s (Cobb?
Jones, by a nose.
Who was taller, Tommy Lee Jones or Sherlock Holmes?
I’ll take Tommy Lee on this one, only because I just think of Sherlock as emaciated, not all that tall.
Whose deadpan delivery has the right combo of funny and snarky, Tommy Lee or Paul Newman?
Tommy Lee.
Who makes a better aging cowboy - Tommy Lee Jones or James Garner?
Real tough choice here. I go with Tommy Lee but only by a smidge.
Which of Tommy Lee’s co-stars is a better match, Will Smith or Robert Duvall?
for my money, WIll Smith
who’s the more talented rapper turned actor - Will Smith or Queen Latifa?
All around talent, I guess it would be Will, although Queen has done some good stuff, too.
Whose portrayal of a major sports figure was more convincing, Will Smith (Ali) or John Goodman (Babe Ruth)?
Well that depends on what you think is more important the rapping or the acting.
I will go with Latifa.
Which rapper turned actor has done more so bad they are great movies, Queen Latifa or LL Cool J?
(I was going to go with a native tongue’s question, but I wasn’t sure how into hip how the players in this game are.)
ETA: DAMN YOU SIMULPOST!
I know next to nothing about rap and am curious about the “native tongue” of which you speak.
I seem to recall at least one each of “so bad they are good” movies involving both your candidates, but not enough to pick one as “done more.” So just to add a new name to the game,
Which rapper/actor is a better undercover cop type, LL Cool J or Ice T?
Ice T.
Who will still be famous 20 years from now, Ice T or Eminem?
Ice T. Eminem was bigger at his peak, but will slip more precipitously.
Who has the seamier past, Ice T or 50 Cent?