If you just want to find the difference between two times you create yourself (for instance to see how long something takes to execute) you could use:
import groovy.time.*
def timeStart = new Date()
// Some code you want to time
def timeStop = new Date()
TimeDuration duration = TimeCategory.minus(timeStop, timeStart)
println duration
If you specifically need to work with the dates as supplied as string above. Try this, first the format of them is a bit odd, in particular the +01:00, which is the timezone, I would expect it to be +0100 for format to work. You could just remove the timezone I just did a replace.
import groovy.time.*
def start = Date.parse("yyy-MM-dd'T'HH:mm:ss.SSSZ","2010-10-07T22:15:33.110+01:00".replace("+01:00","+0100"))
println start
def end = Date.parse("yyy-MM-dd'T'HH:mm:ss.SSSZ","2010-10-07T22:19:52.356+01:00".replace("+01:00","+0100"))
println end
TimeDuration duration = TimeCategory.minus(end, start)
println duration
Outputs
Thu Oct 07 15:15:33 MDT 2010
Thu Oct 07 15:19:52 MDT 2010
4 minutes, 19.246 seconds