Another way is by simulating a million match-offs between $X$ and $Y$ to approximate $P(X > Y) = 0.9907\pm 0.0002.$
set.seed(825)
d = replicate(10^6, sum(sample(1:6,100,rep=T))-rbinom(1,600,.5))
mean(d > 0)
[1] 0.990736
2*sd(d > 0)/1000
[1] 0.0001916057 # aprx 95% margin of simulation error