The wattage and the temperature aren't the same thing. Both a 10W and 80W iron should be run at about the same temperature. The difference is that the 80W iron has more oomph to hold its temperature.
For instance, when you put the piddly little iron on a giant solder tab its temperature might drop so low that it can't melt the solder properly. The 80W would just pump heat into the tab more quickly, so it would get up to soldering temperature quicker. The end result is that you have to hold the litle iron on the piece for longer. The surprising conclusion is that you're probably more likely to overheat and damage something with a low power iron!
Who would have thought I could write so much about soldering
