The difference is 2W. :-)
When we assume that luminosity is related to power (i.e. that the efficiency is about equal, which we can safely assume) then the 1W will obviously be dimmer. But because the sensitivity of our eyes follows a logarithmic curve the difference will be smaller that one might expect. (The difference between 1000 lx and 100 lx is about the same as that between 100 lx and 10 lx.)
The 1W device will become less hot and therefore have a longer lifetime, but the difference may be negligible.
How would you supply 3W to the 1W LED? They might have the same supply voltage, then supplying that voltage it will only draw the current associated with 1W. If you want to have it consume 3W of power you'll have to drive it with a higher voltage. The current will go beyond Absolute Maximum Ratings", and the device will get damaged pretty quickly, possibly break completely. Keeping temperature low is not enough. I don't recommend overpowering it.