You will see no difference between the two PSU's. If the 250 gets the job done, I see no reason to switch it out with the 300, since neither gives you the power to upgrade your system and it won't effect/increase performance by switching.
Power has absolutely nothing to do with performance. If you have enough power it will work. If you don't your computer will shut down as soon as it tries to draw more power than the power supply can supply.
Do you mean increased performance while playing a game? There should be no difference in performance during a gaming session as long as the power supply is capable of delivering the required power to the system.
There is a decrease in performance when a power supply cannot deliver the required power. For example the screen might wobble, then stutter, and finally freeze. The power supply might shut off if there is an overlaod or temperatures get too hot. In a worst case scenario it may blow and fry other components.