I don't see the hex chuck as being all that much of a disadvantage anymore. One can buy regular chucks with hex shanks that snap right in (get the deWalt or the Milwaukee, not the Makita that Home Despot sells--the Makita's shaft has a shoulder on it that's a bit short for most hex chucks and needs some grinding before it will lock in on some drills and drivers and isn't all that great a chuck to begin with).
That said, I'd go with an impact driver over a drill for screws. Reasons? That Milwaukee drill gives you up to 500 rpm and 100 inch-pounds of torque. The equivalent impact driver in the Milwaukee range is a hair smaller, a hair heavier, gives you up to 2000 RPM and
850 inch-pounds and doesn't fight you. You do pay about 70 bucks more for the impact driver though.