First, I have read only secondary works on Rawls and have not read "Theory of Justice" itself, but it is on my list. Unlike Rand, Rawls was an analytic philosopher with a distinguished background, and was among the first to propose ways in which the Anglo-American tradition could revisit "value" questions such as justice, which had long been proscribed by the logicians and specialists.
The book is supposed to be quite rich in itself, full of philosophical excursions, not just a simple plan. His main target is utilitarianism, and I would agree there are many reasons to find utilitarianism unsatisfactory. He attempts to recover something of Kant, without the idealism.
I'm not sure, but I would not call him necessarily capitalist or "objectivist light." His "veil of ignorance" is, I feel, an excellent way to update elements of the Kantian categorical imperative and the "state of nature." His "difference principle" allows for social inequality and hierarchy, only to the extent that it can be shown to benefit the least empowered stratum of society, as in the training of doctors, for example.
So while it is pragmatic, it is fundamentally egalitarian, closer to Habbermas than Rand. The work is complex enough that it might to read and applied in different ways. The Marxist Koji Karatani claims that Rawls did move closer to socialism in his later years and in the introduction to later editions.
I have only read a bit of Rand and secondary texts, so can offer only an "opinion," as some committed Objectivists have hotly reminded me on this site. But as far as I know, Rand did not really engage with other philosophers in any professional capacity. I don't think there is any Rand commentary on Wittgenstein, Frege, Fichte, possibly not even on Kant. It is unclear how much philosophy she read, and I have no idea of she read beloved classics in the original or in translations only.
This is one reason why she is "not taken seriously." Among professionals Nozick was most sympathetic to her and even he didn't find her credible as a philosopher. Certainly, it does not help her case that she wrote capitalist bodice-rippers, purveyed "elitism for the masses," made a habit of rather vile "provocative" remarks in the limelight, and cast a such wide spell over impressionable American minds as the anti-liberal "contrarian" and Nietzschean she-devil of the Chamber of Commerce. But I digress...