Is this compared to the old old udyr or the current one? Also I'm assuming this is about the persistent effect?
Edit: somewhat confused because the new new active is better in literally every way (asp, base and scaling) and you say the new persistent is better.
Being compared to Udyr right now. When I made formulas on Excel, I missed a parenthesis so the numbers I was getting were off.
When I first looked at it, it was taking over 600 bonus AD to have the new Tiger Stance outdamage the new one (which in hindsight is laughably wrong). So scratch what I said about the damage being compared. At 60 Bonus AD the damage of both current Udyr and PBE Udyr will be within one damage of each other assuming you aren't priming the Tiger Stance. So we'll just say they are at equal damage at 60 Bonus AD, number wise. If you are priming the stance, like say to get the Tiger proc while in Turtle Stance thus losing the damage from PBE Tiger's persistent effect, it will take 75 Bonus AD to equal out the damage. Past those points PBE Udyr does more damage with strictly numbers.
This is without resistances, so despite having higher numbers later on, the new version can be outdamaged by the old until you get some sort of penetration, especially against tankier opponents. For instance, you can build a Cloth Armor, and in addition to armor yellows, and the armor mastery, heavily reduce the damage of PBE Udyr early on. You don't get that luxury against current Udyr. As he is right now, Udyr in lane is about dumping damage on them in forced exchanges, and there's no counterplay because the damage is mixed, unless the opposing character themselves counters Udyr. So it was either counter Udyr with your character pick, or lose the lane. Now you can at least build some early armor to not just lose to his damage output.
So given a build of BotRK, and Black Cleaver, with AD Runes, you can expect the PBE Tiger Stance to outdamage the current version especially when you consider penetration. Plus, a single Tiger Stance maxes out the stacks of Black Cleaver because each tick of the DoT adds a stack.
By putting the attack speed completely into the active, it also makes your other stances more effective. You can keep that 70% attack speed going in all of your stances as opposed to the current version which gives a 40% bonus to other stances when dancing. It also makes it far more attractive to Phoenix builds to dance into Tiger. Even without the proc, dancing quickly into Tiger and then out gives you a still hefty 50% bonus assuming you put the standard 3 points into it lategame.
The persistent effect makes last hitting virtually braindead early on, and plays off well with the obvious need for the new Tiger Stance to build a lot of AD. It also makes just staying in Tiger Stance better, which is good because he can't afford to dance too much in lane without Turtle Stance returning mana. By scaling off of Total AD, the current Udyr still deals heavy damage without AD items, plus the diversified damage helps a tanky build do more damage overall. By making him build high Bonus AD to hit high damage numbers, and by making it physical (making penetration needed), it makes building a tanky Tiger Udyr harder. He has to split his gold into high damage and survivability so he is more gold dependent than before, especially compared to Phoenix.