Computer Modern Roman is significantly better then Times New Roman, which unfairly displaced it. The "Modern" in CMR refers to a style now known as "Didone", formerly "Modernist", and is better at typesetting math, and is better at typesetting readable text when you are not cramped for space, such as in, for example, a monograph or an academic textbook.

TNR was designed primarily to not utterly suck at being read quickly when you jam a lot of it tightly together into narrow columns, such as, for example, a cheaply printed newspaper. Funny that, right? A commercially important usecase, to be sure, but not a problem that most of us have.

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Didone style is also expressed in the style known as "Scotch Roman", which is one of my personal favorites, and is easily accessible on web and desktop in the font "Georgia".

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Matter of taste. I find Computer Modern Roman and Georgia to be unpleasantly expanded. My fave is Palatino, but as a second choice I'd rather deal with the compactness of Times New Roman than the expansion of Georgia etc.

I'll allow that an expanded font might have advantages for typesetting math.

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