My experience (born in 1988 in the UK):
Reasonably fluent in both, with exceptions.
Distance. I'll use miles. For measurement, I'll use metres/centimetres. So if I'm measuring up a room, I'll be doing it in metric. For travelling, I'll use miles.
Temperature. I'll use Celsius. A lot of people use both, particularly the generation before mine. I can't use Fahrenheit at all, other than knowing that 100 is bloody hot and that I've experienced in the UK maybe twice in my life.
Quantities. I'll measure my beer in pints but my other drinks will be in litres. Petrol is always bought in litres but I'll convert into (British) miles per gallon quite readily and on-the-fly.
My weight and height, I'll use Stone and Pounds (16St 7Ibs) (6"2') but for any other weight I'll use (mostly) kilograms, even when I'm cooking.
I can use both but I'm more comfortable with one over the other most of the time. Those are my preferences and I think they're fairly reflective of most people my age in the UK - although I'm quite happy to be proven wrong there. Generally speaking, it was Metric at school and Imperial at home. My parents are definitely more 'full time' users of Imperial than I am but can also use both. My grandparents are mostly Imperial but my granddad worked in a physics laboratory for thirty years during the changeover so will mix and match his units too.
In terms of what I find more useful, I'll say that Metric definitely has a lot of advantages because of it uses a standard mathematical base (decimal). The problem with Imperial is the shifting mathematical base that requires you to know the units. For instance, 14 pounds in a stone but 12 inches in a foot, with three foot in the yard. It's not difficult to use Imperial if you know the units well and you've used them a lot but Metric is intuitive.
It's a bit like when the UK shifted over to decimal currency in the early 1970s. 240 pennies to the Pound Sterling, with 20 Shillings of 12 Pence is pretty easy to remember (then add in things like Crowns, Guineas, etc) but to somebody coming to the UK, it could have been baffling - most currencies have been decimal for a long time. Like everything else, having a non-decimal currency has its roots in history (a Pound Sterling at one point literally meant a Pound (weight) of 92.5% purity silver and it was easy to divide it into 20 and then into 12) but doesn't make a lot of sense without that context.
I'm not saying one is better than the other but Metric certainly has mathematics on its side.