Cary Grant did not receive an Oscar nomination for portraying Johnny Case in Holiday or Dr. David Huxley in Bringing Up Baby.
Grant is Holiday also is in a comedy, but not a screwball comedy. There is a certain Frank Capra style edge to the material that involves Grant's character Johnny who wants to go on a holiday early in his life then work later on. This does not mean the meat of the film is serious by any means, and there are plenty of comedic moments in this film again. Grant here again is very charming, although in that slightly more serious charming Grant sort of way. There is not that constant flamboyance found in his Baby performance and Grant gives a performance that mixes up some quieter serious moments with more energetic scenes, which actually does quite well although I do believe he is funnier in Baby.
His chemistry with Katherine Hepburn is also very different in both of the films as well. In Baby they pretty much are there to one up one another in terms of their comic energy. In that case they are very enjoyable together as Grant plays his part as someone who only increases in disbelief and their relationship is built on the insanity they get into that results in many mishaps, but by the end they love each other. They really do not have any romantic scenes other than their last one, but what they do works for the film. Holiday it is far more gentle and underplayed as it has to be as Hepburn plays the sister of Grant's fiancee in Holiday. They have great chemistry there to and develop the underlying connection between their characters in an effective fashion that work properly for the conclusion of the film.
Both performances by Cary Grant are great examples of his on screen abilities whether it is his frantic and very humorous, or calmer and rather humorous. Grant in both cases gives a very charismatic turn that infuses life into each of his pictures with his expert comedic timing. In Holiday's case he handle the character's struggle to support one's own dream well with just a quiet but passionate determination. In terms of what performance I think it is better, well that's a little difficult. On one hand Holiday does require more range from Grant as he has to sell both the funny and the serious scenes which he does. Bringing Up Baby requires him just to be funny, which he is. Well the complexity of the role does not always mean the better performance though, and I do think I slightly prefer his just plain entertaining performance in Bringing Up Baby.