Quantitative (continuous) traits are preferred because they contain more information. However, we are strictly referring to quantitative traits that already follow a data distribution that can be modeled in whatever it is your proposed statistical test. Usually, this would mean a Gaussian / normal distribution. If you have a very weird variable that has a skewed distribution that cannot be modeled, then changing it to qualitative (categorical) would be better.
Think about it: we have a beautiful variable of n=1000000 and it 'perfectly' follows our expected distribution (in R):
million <- rnorm(1000000)
Now lets dichotomise it:
million[million<=2] <- 0
million[million>2] <- 1
They look completely different and you can see that we have lost so much information. Whilst we can treat this new data as categorical, you can clearly appreciate at the same time that we have thrown out so much information.
It is this lost information that increases error (type II) and, therefore, reduces statistical power. Remember that, generally speaking, statistical power is the level of our ability to identify an effect when an effect is actually present in our cohort. You can therefore appreciate that, by throwing out useful information, we are reducing our power.
PS - wrote a bit more here: A: Log-tranformation and GWAS