The US would not have developed as fast if it had continued to be a British colony. A major cause of the War of Independence was that when Britain took control of the Ohio after the French and Indian War, the crown claimed the right to all negotiations with the Indian tribes and prevented the colonists from buying and/or seizing Indian land in the Ohio River Valley. Recall that Washington had been to the headwaters of the Ohio. He and others were well aware of the rich lands west of the Appalachian chain. Also, many of the financiers of the war were also land speculators before and after the war. The officers of the war formed the Society of the Cincinnati, and many of them were granted land west of the Appalachians.
The net result was the rapid expansion westward from 1790 through the 1800s. This expansion and development of the lands, forests and mines was aided by rapid immigration from many countries in Europe, not just the British Isles. As a British Colony, the US would not have been as available to other Europeans, and development would have been slower.
Possibly slavery would have ended more quickly, but Britain also supported the South, rather than the North. The South's cotton fed the British textile factories. After the Civil War, Britain went on to develop cotton plantations in Egypt as a replacement source.