Throw depends,...
NOT on lumens,...
BUT on surface brightness of the source, short arc, then HIDs (and their permutations) and then Halogens (the more overdriven then better). It's all a function of surface brightness of the source.
And actually, IIRC, a shallow reflector will give a tighter hotspot since it's a segment of a "larger parabola" while a deeper reflector (part of a smaller parabola and thus increasing the source to reflector ratio) will give a bigger hotspot.
Design tricks for reflectors are great, but in general HIDs and halogens have similar hotspot sizes so it doesn't matter. Maybe for a short arc.