I've got a couple of decent badger brushes and they're pretty forgiving on the face, even the floppiest ones I own. I've recently sold on my synthetic, though that's because I have too many brushes and simply prefer the look of the ones I own. I find them just as good for lathering, whether in a bowl or on the face plus it adds an extra dimension to my meditation-esque shaves. Drying them off with a comb and hairdryer just adds that extra relaxing step to my shaves.
I don't think I'd hesitate to buy a synthetic again down the line, or re-knot an existing brush with a synthetic knot (an idea I'm toying with currently), and would happily recommend them for new starters. They're definitely soft, strong and capable that's for sure.
As for the badger brush you've got, I'd assume it's a little lofty, and probably has some 'scritch' to start but will soften up over time as they tend to split hairs in use. If you want a great take on an inexpensive (for the quality) brush, the Maseto 30mm 2-band finest is a great way to go - there's a thread dedicated to it on this site.