You'd get lower efficiency as your components will only consume the PSU's amps/watts that your rig uses.
Generally, the highest efficiency in PSU wattage curve is where you are using 50% of the PSU's rated power. As such, if say, your rig is drawing an average power of 225W, then the 450W would be the most efficient PSU. If a rig is drawing less or more on the wattage curve, the efficiency is lowered. So, if you are drawing 225W on a 1000W PSU, that's only using 22.5% (lower efficiency).
Another thing is cost/performance. Getting a 1000W PSU and you have...