Using just his E as an example, Vlad's rework made him less stat-check.
Old Vlad presses E and gets stats from it, stacking up to 4. If you're in range, you take unavoidable damage, if you're outside of the range, you don't take damage. That's it.
New Vlad has to hold E and gauge how much health he wants to spend, and how much damage he wants to do, at once. New E has a charge-up time to warn enemies to leave the area before it goes off. New E can be blocked by tanks/minions/pets/Heimerdingers.
Onto his Q.
3-hit passives are good design, if overused. The idea being that 50 dmg + 50 dmg + 50 dmg provides less gameplay interaction than 20 dmg + 20 dmg + 110 dmg. The latter makes players feel good about landing the third hit, and rewards enemies for not letting themselves take the third hit.
Usually with three-hits, there's an indicator that allows the enemy to react accordingly to avoid the "big third hit", which the Bloodthirst bar (which everyone can see) does have. Q - Q - Crimson Rush is fairer for Vlad's opponent to react to than Q - Q - Q - Q - Q - (repeat infinitely) and it's more enjoyable for Vladimir to strive and achieve those Crimson Rush Q's rather than just Q infinitely and abuse the cost-less nature of the spell.
Old Vlad would EQEQEQEQEQEQEQEQEQ until something ran out of health. If you were in his range, you took damage and that's that. New Vlad has to manage his Q's better because half the time they're shit and the other half they're great, and has to properly position as well as gauge how much his E is going to cost him/damage enemies, while still giving opportunities for the enemy to react before the E goes off.
Old Vlad would forget-fire his ult and let his team do all the damage. New Vlad is incentivized keep fighting and survive just long enough to get the heal-pops from his ult, putting him in harms way and allowing the enemy some chance to cut him down before he gets his second wind.
For the love of blood, I cannot understand the position of "new Vlad is worse in terms of stat-checking than old Vlad". It's simply not true.