I've never sparred a straight boxer (in a boxing gym), in boxing only. Because I've only ever trained at jits/ MMA places.
That said, I normally do pretty well with straight boxing (at least at Xtreme Couture and the gym i'm at now), I just turn my left shoulder in a bit more and have a more linear stance. I like that I can put more torque into my cross, it feels ALOT more powerful from a boxing stance.
Also, i'll offer a bit of a topsy- turvy version of your experience:
After a few months of training in MMA (probably 3-5 striking classes a week, boxing or MT) I ended up sparring a guy in Muay Thai who came from a strong boxing background. Real stoic Russian guy, a littler smaller than me (i'm 6'2 220). But I digress.
Well anyway, he basically admits to me that he's never really trained kickboxing, and although I don't consider myself as someone with killer kicks, I can kick high and I do have decent snap/ technique. So any way, after warmup/ drilling/ bagwork, we have 15 minutes of sparring, 3 minutes on 1 minute break, until class was over.
So right off the bat, I can tell this guy has fast hands and good footwork. As such, I keep my hands high and tight, and don't get wild. Well, the only problem is that he really isn't standing in a kickboxing stance, he's still stuck in boxing mode. So every time he gets in range and plants himself to throw, my shin was already digging into his thigh. Must've dropped the guy like 4 times throughout 3 rounds, just from leg kicks. And not even like I was being a dick and kicking real hard, they just caught him and knocked him on his ass.
And when he finally started to square up (in the 3'rd round or so), I started tagging him with punches. Every time i'd come in, he'd lift the leg to check and i'd tag him with a cross.
So I guess the moral of the story is that both games are different. I'm sure i'd get taken to school in boxing by the amateurs in the boxing gym that shares the building w/ my jits gym up here at school. But I also think I could really hold my own against them under FTR sparring.