Although there were substantial casualties among British troops who fought both the French and Indians, and Britain certainly bore most of the financial burdens of the French and Indian War, American colonists, both those who fought as part of the military and civilians, probably sacrificed far more than Britain did.
One of the principal effects of the French and Indian War for colonists was terror. The French, as part of their military strategy, used their Indian allies to create a war of terror against English colonists from the East Coast to the Upper Midwest. And, as we now recognize, a war of terror may not necessarily result in massive casualties, but its psychological effects are devastating, especially when one considers the methods of Indian warfare, which included torture and mutilation. The threat of an encounter with Indians, therefore, was almost as effective as an actual encounter, and this threat caused thousands of colonists to abandon their homes, often during winter.
From a social and cultural standpoint, while the British suffered substantial military casualties, American colonials suffered significant military and civilian casualties, as well as widespread destruction of homes and businesses throughout colonial territories, resulting in a social and economic disruption that took several years to remedy.
The fact that Britain was carrying on a world war is relatively meaningless to American colonists. All wars, like politics, are local.
I would argue that the British people sacrificed more for this war than the colonists did, though there are points to be made each way.
For the colonists, the major point is that a higher percentage of them fought in the war. It is said that more than a third of the men of military age in New England fought in the war. This is surely a great deal higher than the proportion of British men who fought in the war. On a per capita basis, then, more colonists were in the war.
Financially, however, it was surely the British who sacrificed more. First, we need to remember that this was just one part of the Seven Years War which was something of a world war. This meant that the war cost a tremendous amount of money. Taxes were raised to pay for the war, but those taxes applied only to people in Britain, not to the colonists. This financial sacrifice was quite significant and probably had a greater impact on British people than the war had on the average colonist.
The colonists did because they were the main ones fighting for Britain. Britain also lied about covering all of the $$$$ for the war because they were in debt themselves. So, in turn, Britain heavily taxed the colonists to increase their revenue. Also, there were cultural gaps that caused issues between Britain and the colonies so the colonists were sometimes abused by British commanders. Overall, the colonists took the hit when it came to fighting, and Britain took it financially...