The biggest downside I have experienced from the cheaper flux core welders is that they have a much lower duty cycle. They work great for learning the basics regarding technique and power settings (obviously you won't learn anything about gas flow) and for thinner sheet metal, but wear out quickly if you try to weld a bunch of, say, 1/4" thick angle iron. Ask me how I know.
It all depends on what you're looking to get out of it. If you are just wanting to tack some stuff together and it doesn't need to withstand a lot of abuse or look pretty, flux core will do just fine. If you are looking to do more structural welds, a GMAW (Gas Metal Arc Welder, formerly known as MIG - Metal Inert Gas) Welder is more what you're looking for. I say GMAW because CO2 isn't technically an inert gas, but can still be used with a "mig" welder, so they changed the name a couple years back even though 99% of people still call it MIG.