User blog comment:Centuriarch/Jayn, the Huntress/@comment-7709681-20150112042317/@comment-24036535-20150113023047

Well, to be quite honest, making only one ability apply on hit effects DOES ruin the entire essence of the passive, it's the ONLY real difference besides tweaked damage.

Let's crunch some numbers shall we? I'll go to level 18, assume four damage items, with Berserker Greaves and GA as final items. Vital Stats info below:
 * hp          = 476 (+87)
 * mana        = 232 (+69)
 * damage      = 50.6 (+2.35)
 * range       = 475
 * armor       = 32 (+3)
 * magicresist = 30
 * attackspeed = 0.645 (+2%)
 * healthregen = 6.5 (+1)
 * manaregen   = 6 (+0.8)
 * speed       = 330

Assuming AD build, oriented to AD:

IE, BT, LW, PD.

80+80+40+93(base)=293 AD, 55% crit, 35% armorpen, 70% bonus AS.

Average damage=(293*.3)*1.825(Average DPS bonus from crit, accounting for IE)*3(Three strikes each)+~488 damage from the initial auto, maybe more, maybe less, depends on crit.

Assuming On-hit build:

Wit's End, Bortk, Statikk Shiv, Muramana.

25+29(Muramana Passive)+93(base)=147 AD, 20% Crit, 122% bonus AS, Initial damage of Muramana's three charges: 252, Wit's End: 126, Shiv initial damage: 100, Bortk: >15% target's current health.

Average Damage=(147*.3)*1.2(No IE to mod crit)*3(strikes)+252+126+(100*1.2)(Shiv)=~657 Initial Mixed Damage, plus ~15% of targets max health, and superior attack speed.

It should be noted, 246 of this damage is magic, while the other portion is physical, which gains no penetration in this build. Muramana, and Bortk damage both only decrease from there, and I can certainly gut her mana even more if the need be, its rather high for a marksmen. This also does not include Jayn's Ult, which would grant AD Jayn a significant steriod. Looking at numbers, On-hit looks better, and likely is, but AD is not far behind, and her scalings, ult, and penetration could make the point that AD IS slightly better, at this point I'd leave it to personal preference. Remember, this is damage on the initial auto attack.