Would I notice a difference if I upgraded from a 300 watt mono amp to a 800 watt mono amp?

You will notice a difference, but not as dramatic a difference as you might think. Mostly you will notice that the sound at lower to midrange levels will be cleaner. The other consideration is to make sure your speakers or drivers can handle the wattage. If your sub-woofers are only rated to 300 or 400 watts, you will eventually end up degrading or even blowing them out. Since your sub-woofers are currently rated at 600 watts, (by the way is that RMS wattage or peak to peak?) you could notice some signal degradation at the upper levels. Just to be safe, I would check with the manufacturer, or the store that sold you the equipment to make sure you are not voiding any warranties or anything. I don't know the reputation of the Bazooka line by the way, but I have been using Pioneer equipment for years and absolutely love that brand. You might simply need to put a small resistor on the connection to prevent overload. It shouldn't be a big deal.