The differences are minor, but there are differences. When brewing normally, water begins to drip through the paper filter immediately when poured over the grounds. After stirring I usually have to add more water after the bloom recedes. Inverted, all the water stays with the grounds until you flip it over and start extracting. The extra water added with the normal process is hotter, and I believe will tend to over extract bitter notes more easily, not only because of the higher temperature, but by virtue of the added volume of water passing through the grounds.
Inverted, however, the volume of water is less, and because of that, the temperature of that water will be lowered a bit. You can extract quickly, or wait as long as you want to extract the coffee. Additionally, I have seen it claimed that with the inverted method, oils that will rise to the top of the column will be forced through the filter first and flavor the coffee more than with the regular method where they tend to get trapped in the grounds.
I have gone back and forth but always seem to go back to the inverted method. It provides more control of the variables and for me gives a better flavor, even when using the same beans, same roast, same water temperature. Your mileage may vary of course.