Coding genes are subject selective pressure that are not present for pseudogenes, that would suggest that pseudogenes have a higher mutation rate than coding regions. If so, how much higher?
It is important to distinguish between the rate of mutation, which is a biochemical process, and the rate of fixation, which is a population process whereby an allele with a particular mutation becomes fixed (present in all individuals) in the population. Relaxed purifying selection, such as that experienced by genes undergoing pseudogenisation, affects the fixation rate of mutations because new variants are not being filtered from the population by purifying selection. The mutation rate itself is probably constant, unless some other factor is at play.
In response to comments, I will say this: if functional constraints on the gene are relaxed to the point where all mutations are selectively neutral, then the process of mutation and substitution can be modelled by neutral theory and the expected rate of substitution (or fixation) is the same as the rate of mutation. This rate is dependent on several factors - lineage, life history, etc., and the difference between this rate and the fixation rate for a given coding region is dependent on the severity of functional constraint on that region.