It is very hard since 4.11, Because as AD dps is much more better to play Zed or something like that on mid, AD Kayle was good in season 1-2. AP was strong since season 3 to half season 4, but what now? It is rly hard, I hope that rito will buff hybrid items and add some more interesting hybrid items because nerfed AP is atm much stronger than Hybrid one. I am not afraid to say AP is still strongest even after these nerfs. Bruiser is kinda OP but not in soloQ (it needs big teamwork), so bruiser kayle = ranked team only. AD needs a little buff, AD rate to W or something like that and hybrid build needs more buff, even if she has got hybrid rates, it is not as strong as you may read from abilities description. The Item which is best on Kayle (AP or atk speed) atm is Wit's End. Why? since it deals only 42 dmg on hit, it is not that much, but with 2,3 atk speed? (easy) - Let me calculate it: E deals 25% AP dmg right? So to deal 42 dmg with E you need 4x42 AP = 168 AP, This item worths 168 AP with E and something like 70 AP with Q. Keep on mind that it has kind of pene which stacks with passive and the magic resist. It would be relly stupid not taking this item immediately after nashors.

Well they don't know how she became what they made her become, lol... look at her patch history, since her last rework it was a continuous general buff, on top of all her E AP ratio increased from 0.2 to 0.4, with this motivation: "Kayle is not a toxic champ, we don't mind making her viable". Totally no sense buff and reason, because she was already perfectly good, but just unpopular, and it was against the main reason of her last remake, which was to nerf her late and to buff her early. Now she got her early buffed and her late too. I love her as a champ able to do more roles, IMHO she is supposed to be good at everything and master of nothing, so she hasn't a really specific weakness like a specialized champ. If they think her power is no longer acceptable, maybe it's time to bring back the old numbers, maybe?

If you want to do max physical damage with her, you should build Infernity Edge and Trintiy Force first, the most situations you have to deal damage you just can do some hits. And as more damage you can do in the first second as better because your target goes faster down and cant do anything anymore. Thats also why you should not max Righterous Fury first.

DPS usually is slow, lower in the begin but higher in the end.
Burst usually is fast, higher in the begin but lower in the end.
The "blue point", where DPS surpass burst, is very much situational.

Since the low range on AAs and the good sinergy between LS and Intervention (you can heal while invulnerable and keep attacking), I suggest to leave Infinity Edge as last item and go for a solid LS to better fit her good duelist capability.

Trinity Force and Lich Bane mainly improve the burst damage, but you haven't abilities to spam to easily proc indefinitely Spellblade every 2 seconds, which is a very important part of those items. If you try to proc it efficiently in 6 seconds with your abilities, the sequence is inevitable Righteous Fury -> Reckoning -> Divine Blessing, then you have to give up Q in the first 2 seconds, with all that this entails. You can get a really better result with CDR, but I still don't find them a good choise, Kayle hasn't a kit to be a very good burst champ.