Yes, they profited much more from sugar, and they still abolished slavery in the Caribbean. The anti-slavery lobby was very powerful in Britain.
But the price of sugar was very low at the time of abolition, meaning the planters took their chance to get a decent chunk of compensation versus an uncertain future on the sugar price. There would be very limited opportunities to get a low price of both sugar and cotton, although it's possible they might ban it anyway despite a high price.
There's also the case that the Caribbean islands were much more dependent on the British Empire for supplies than the continental Southern colonies.
On the other hand, cotton is much more dependent on Britain as a market (due to it being vast bulk of the world's industry) than sugar (which was consumed everywhere). This effect is even stronger if New England is part of the British Empire. Going to war with your only customers isn't the brightest idea. But then, going to war with the much stronger northern half of the country isn't a good idea and the firebreathers still did that...
A lot will also be related to voting reform. Once non-conformists and the middle classes get the franchise it's a lot harder to stop abolition. The type of setup that avoids OTL American revolution will also matter in terms of the agreement between division of power between Westminster and local assemblies.