This is an interesting question and we should probably have a statistical geneticist around, so further answers may show up better than this one. So I'm also assuming the question is: Is the rate of variation on the X,Y and autosomal chromosomes different? Also assuming XY male heterogamy as humans have - different sex chromosomes will give different results between male/female.
The main distinction being - if males absorb more mutations on X as well as Y, then it would be nigh on impossible to see this phenomenon statistically since those chromosomes get passed on to females immediately.
Its important to remember that some of the X and Y regions do recombine even in men in the pseudoautosomal regions. The Y also maintains itself with a self-recombination event in meiosis. So the message here applies to the SDR (sex determining regions) of the X and Y chromosomes - other regions are quite possibly not different than the other chromosomes.
Anyway I've found this modeling paper "Patterns of Neutral Genetic Variation on Recombining Sex Chromosomes" which estimates and compares the relative coalescence time for variations on the autosomal, X and Y regions.
In any case the models in the paper says 'yes they are different and Y non-autosomal regions accumulate variants faster'. The coalescence time is the amount of time for a variation to spread into the general population on one of these 3 types of regions.
In cases where there is neutral selectional pressure "Close to the SDR, expected coalescence times are shorter on Y chromosomes and longer on X chromosomes than for
Which is to say speeds for incorporating variations are Y > X > autosomal
Note that the paper goes on to say that when there are more than one competing versions of the Y chromosome in a population (which seems likely to be the case), then the spread of variations on the Y goes to a normal autosomal rate.
So its likely that this effect is small overall.
It has been documented that some Y chromosomes are very competitive though.