A really silly question here but

Regardless of talent or quality of teaching , just talking physically.

What are the differences between a child aged 8 and one 11, in terms of power, ability to sustain long notes (physical like lung capacity.) Or are they much of the same?

"How long is a piece of string?"
It of course depends on the individual child and the stage of their physical development (and also whether they are a boy or a girl - the latter can be roundabout 2 years ahead with regards to the onset of puberty, so I'd expect many 11 year old girls to show vocal changes of some sort, but not necessarily every boy).

Generally speaking, I would (vocally) treat most 8 year olds like children, and most 11 year olds like adolescents to be on the safe side - that's just a general rule though and can vary wildly individually:
I teach two 11 year old girls at the moment, one much closer to what you'd expect of an 8 year old (really small, completely unchanged, clear treble voice), the other already with the typical adolescent problems (very breathy, slight loss of top range etc). There are simply no hard and fast rules. For that reason, generalisations always make me a bit uncomfortable.

Children of course have smaller lung volumes, and they don't tend to have the full dynamic spectrum available to adults. Their voices are, in a way, more robust though than those of adolescents (if you respect that they are still children's voices nevertheless).

Girls roundabout 8 usually have slightly smaller lung capacities than boys of the same age - some studies suggest they are able to create more expiratory flow (but less pressure) though, one explanation being that their airways are possibly a bit wider than those of boys at that age. Their expiratory flow and total lung capacity also tends to increase faster than that of boys between the ages of 8 and 12. The boys of course make up for that at a later stage, but then we're leaving the age-bracket you mentioned.

So the changes in lung volume and expiratory flow between the ages you mentioned will be somewhat apparent. More expiratory flow doesn't necessarily mean better/longer phrasing though, because this also depends on the ability to "work the whole system" (with the vocal folds as the valve on top, which can be a bigger problem in adolescents than children because of the laryngeal development). There will of course also be a change in vocal tract length when the child grows, which will also change the sound in acoustic terms. How much again depends on the individual.

So to cut a long story short: Impossible to say for each individual, but generally speaking, you would expect a slight difference. The child will have slightly less dynamic control (this includes "dropping off the note" due to not really noticing how long the breath will last), a higher voice and a generally smaller range than an ADULT. Compared to the adolescent though, their range can (not must!) actually be bigger, their voice might be clearer and overall easier to handle. I wouldn't want to say though there HAS to be a massive difference between 8 and 11 in any given case.