Actually, an interesting question.

Assuming that equal pressure is applied,(unlikely but what the hell...):

Take the dia. of the small straw as 2 unit, the larger at 4 units.

This gives:
Area Cir. per. of Ratio of
channel Area/Per.
Small straw; 1 Pi 2 Pi 2 Pi. 1/2
Large straw; 4 Pi 4 Pi
Outer Ch. ; 3 Pi(L-S 6 Pi(L+S) 1/2

Neglecting boundary layer width as a factor, (its effect being
dependant on flow velocity and we don't know it anyway), the
resistance should be the same.
I would guess however that the boundary layer width in the
narrower outer chanel would govern.