Single Target DPS: Elemental Hit vs. Frenzy

So basically the comparison should be between:
1) elemental bow - with elemental hit
2) physical bow - with frenzy (7 charges) and cold arrow used when on full charges (because cold arrow uses like 40% of conversion)

To rule out speed - let's say both bows has same speed.
To rule out support gems - let's say both use faster attacks and elemental dmg and (cold or elemental hit - depending on case 1), 2))

Let's say all gems will be lvl 20, no quality.
Let's say the gain from 1 average elem dmg for case 1) will be 10 DPS. For case 2) this will have to be somehow accounted for increased speed from Frenzy.

I think we should try to compare on these basis for some overview of the DPS difference.

That seems relevant, yes.
I think we can consider having 7 frenzy for elemental hit, but then less elemental dmg bonuses maybe.
If someone wants to spend some time with theory to get numbers, or more useful, someone want to try this ( I use the 25%chaos dmg bow so ... ), that could be useful here =)).
But anyway, for efficiency matetrs, each one would have a different build that goes with it.