Rashford is an excellent passer. Sancho's close control is much better, yes.
Again my worry with Sancho is not his ability to link play, he's very good at it. It's his ability to beat a man against low blocks. Players like Mane have shown just how important that can be over the last couple of years. In that sense, I see more of Mane in ASM than I do in Sancho. Also ASM is not the headless chicken you make him out to be. His passing and finishing are very good.
If Sancho's dribbling was just a bit more explosive ala Neymar I'd have no qualms spending the £100m+ on him, as it stands it makes me worry a little at that price.
Sancho is a better dribbler than Rashford. Just compare his dribbling numbers to great dribblers who made the transition from another league to the PL. All of them struggled in their first year in the premier league in terms of dribbling, but then took it up a notch bettering their own younger dribbling numbers. I don't see why Sancho wouldn't be the same.
I posted these a while back so now they're out of date as Sancho has another season under his belt.
per 90 (successful/attempted/%successful)
Sancho age 18: 4.1/6.8 / 60.3%
Sancho age 19: 3.0 /5.4 / 55.6%
Hazard age 19: 2.0 /5.3 / 37.7%
Hazard age 20: 2.9 /6 / 48.3%
Hazard age 21: 2.5 /4.9 / 51%
Hazard age 22: 2.1 /4.4 / 47.7% (Premier League)
Hazard age 23: 4.1 /6.5 / 63.1% (Premier League)
Sane age 19: 3.3 /6.8 / 48.5%
Sane age 20: 3.5 /7.7 / 45.5%
Sage age 21: 2.7 /4.8 / 56.3% (PL)
Sane age 22: 3.2 /4.9 / 65.3% (PL)