"Contrast the Democratic party nominating rules with the Republican party nominating rules in New York. Which set of rules used advantages the front-runner more, the Democratic party rules or the...
"Contrast the Democratic party nominating rules with the Republican party nominating rules in New York. Which set of rules used advantages the front-runner more, the Democratic party rules or the Republican party rules?"
The Democratic Party primaries are all proportional in some form: If you get 30% of the votes, you get 30% (or so) of the delegates.
Some Republican Party primaries, including New Jersey, are not proportional but winner-takes-all: If you get more votes than anyone else, you get all the delegates. Others have high thresholds for getting delegates, which has a similar effect.
The general election is also winner-takes-all, for both parties.
The winner-takes-all system gives a substantial advantage to the front-runner relative to the proportional system. The threshold system gives a smaller but still significant advantage to the front-runner over a true proportional system.
Let's take a look at the actual results for New Jersey, shall we?
In the Democratic Party, Hillary Clinton received 63% of the vote and Bernie Sanders received 37% of the vote. Clinton got 85 delegates, which is, sure enough, 63% of the allocated delegates; and Sanders got 49 delegates, 37% of the delegates.
In the Republican Party, Donald Trump got 81% of the votes, John Kasich got 13% of the votes, and Ted Cruz got 6% of the votes. But Donald Trump got 100% of the delegates, all 51 of them. Had they been allocated proportionally, Trump would have only gotten 41 delegates, while Kasich would get 7 and Cruz would get 3. Over many states, that difference can add up to a substantial advantage for the front-runner.
You asked about New York specifically though.
The New York primary is also proportional for both parties, but the Republican Party has a higher threshold for delegates. As a result, it behaves more like a winner-takes-all system.
Hillary Clinton got 58% of the votes, and 56% of the delegates. Bernie Sanders got 42% of the vote, and 44% of the candidates. The rounding was actually slightly in favor of Sanders.
While Donald Trump got 60.4% of the votes in New York, he got 89 delegates, which is 94% of the delegates! This happened because only John Kasich beat the threshold for getting any delegates, and only barely, getting 25% of the vote and only 6% of the delegates. Ted Cruz got 14% of the vote but no delegates at all.
It's not quite winner-takes-all like New Jersey, but it's quite close.