There is no difference in the gas as such, CO2 is CO2. However, pressurized CO2 is a lot more controllable and you can get a lot more CO2 into the water because of the way it works. Also, pressurized CO2 needs a lot less intervention.
Pressurized CO2 is a lot more expensive to set up, but once you have done so, it's easy to run and maintain. I only need to exchange the tank once or twice a year.
To put it differently, plenty of people have gone from a yeast and sugar method to a pressurized tank, but I don't know anyone that's gone the other way.
CO2 gas is the same whatever the source, however, yeast do not produce 100% pure CO2. They produce other gasses as well, and most of the gas that enters the tank is nitrogen (from the atmosphere). This means that the concentration of CO2 gas that yeast puts out is quite dilute compared with a pressurized CO2 tank. I would estimate that the CO2 % in the gas yeast releases is probably only a few % compared with 100% CO2 in a pressurized cylinder.
The concentration difference, ease of use, lack of yeast container explosions, cheap refill cost vs. cost of sugar, and consistency make pressurized CO2 worth every cent and far superior in every way. There is no comparison between DIY and pressurized, the difference is like light and darkness.