Comparing outliers in two distributions I apologize in advance as I am not well-versed in statistics, but I hope that this question makes sense.
I have 2 populations which are normally distributed and have a near-identical mean. I would like to know if the upper quantiles (say >0.99) differ - ie, does one population extend further than the other, and how can I see if the difference is significantly different?
One approach I have thought to take is to subset my dataset on just the upper quantiles, then plot the ECDF, but I don't know that this is a correct approach.
 A: Two samples of size 1000 from the same normal population.
set.seed(2022)
x1 = rnorm(1000, 50, 7)
x2 = rnorm(1000, 50, 7)
q1 = quantile(x1,.95); q1
     95% 
61.17923 
q2 = quantile(x2,.95); q2
     95% 
61.98871 
dq = abs(diff(c(q1,q2)));  dq
      95% 
0.8094812 

Is this an unusually large discrepancy?
set.seed(106)
m = 10^5;  dq.95 = numeric(m)
for (i in 1:m) {
 x1 = rnorm(1000, 50, 7)
 x2 = rnorm(1000, 50, 7)
 q1 =quantile(x1,.95)
 q2 =quantile(x2,.95)
 dq.95[i] = abs( diff(c(q1,q2) ))
 }
mean(dq.95 >= dq)
[1] 0.22008

No. Not unusually large; about 22% of such comparisons
have 95th percentiles farther apart.
hist(dq.95, prob=T, col = "skyblue2")
abline(v = dq, col="red")


Note: As you might guess from the histogram, the
distribution of the 95th percentile of a sufficiently
large sample is approximately normal. The variance gets
larger for percentiles in the far tails. This CLT for
quantiles (except the min and max) a fundamental
result in the theory of order statistics. Depending
on the circumstances of your project, it might be
worth your while to see if your samples are large
enough to use this asymptotic result.
