Eli's was more efficient. Of course it should have been, given that he had a few thousand years of technological progress under his belt.
As for timing, one decade is easy, two is marginal but possible, but three or more decades would only be possible if something weird were going on. Maybe someone invents an inefficient but workable cotton gin, which puts further inventors off the subject for a time without allowing the massive boom of OTL.
There's one major consequence of this that bears discussion and is virtually never considered. The sudden dramatic upswing in slave prices due to the cotton boom didn't just strengthen slavery in the south; it also killed it in the north. So many people sold their slaves south as the price went up that there were no longer enough northern slaves to sustain the institution.
If you can delay the cotton gin by 2-3 decades the free/slave divide will be unrecognizable. Massachusetts and Vermont had banned the institution during the radicalism of the early revolution, and so, theoretically, had New Hampshire, though a bare handful of slaves lasted almost to the civil war there. Pennsylvania had entered into a much more considered and significant effort in 1780, setting up the gradual abolition of its (much more substantial). Connecticut and Rhode Island followed four years later. The cotton gin was patented in 1794.
Now, New York began gradual emancipation in 1799, New Jersey in 1804. That may be slightly delayed without the cotton gin, but it wouldn't be more than a year, so forget about it.
What would be relevant would be if the gin were delayed more than two decades. That would put it up to the era of Illinois and Indiana becoming states. There was serious talk in OTL of legalizing slavery in both states historically, and I suspect that it would have come about had the north not emptied itself of slaves a generation prior.
When the cotton gin does appear it will leech so many slaves that one or both states may well end up abolishing the practice late in the game, but in the meantime.... For starters there's no Missouri Compromise because it will be taken for granted as a slave state. Texas may also be admitted earlier absent the competition streak in the senate, but that's assuming low butterflies. It's hard to say what would happen in Kansas for much the same reason.