This is a good question and I'm sure you're going to get differing opinions on this.
It's my understanding that the flux core welder uses the flux to purify the weld just as the gas is used to purify the weld when using a conventional mig welder.
The argument and where people have a difference of opinion as to how well the flux core wire actually purifies the weld. Some will say not well at all and others will say it does the job just fine. All I can do is relate my experience. I use a Lincoln weld pack 100 flux core welder exclusively and I've done everything from light sheet metal to 3/16" steel including frame work. From what I've seen the welds, although certainly not as pretty, are just as strong as a gas weld. I get good penetration and other than the spattering caused by the flux I can see no difference. I generally grind my welds to dress them up so the spatter doesn't bother me much.
That's my experience so if it was me, I wouldn't worry about it. Now I'm sure there are going to be some descending opinions coming.....