Any attack that hits someone who uses a d4 for HP is meaningful
This is either wrong or intellectually deceptive, depending on whether or not the error is intentional.
The difference between D4 and D10 is 3 * (level + 1) just going off of straight dice. However, as you get Con mod to that, this is not as big of a difference as it seems. Most likely, after the initial level or two the difference comes out to be beatstick has a third more HP.
However, there are several factors to consider.
1: Wizards are rather SAD. Even on 25 PB they can run Con 14, have their Int high or maxed, and not lose anything. Meanwhile the beatstick classes? MAD. As a result the Wizard might have a better starting Con score, which would close that gap somewhat.
2: Wizards are fairly gear independent, but can make their own gear. As a result, the Wizard has far more cash to devote to secondary purposes like Con boosting at any given time, and will therefore hit any given breakpoint sooner. Until maxed out, this again means more Con for the Wizard. And if you're paying attention at home, it only takes a 6 Con differential to close the gap to... 3 HP. More likely you only end up 2-4 ahead.
3: Wizards are very good at not being hit. They don't have to be right in front of the enemy to be relevant, they don't have to move 5 feet or less a round to stay relevant and most importantly, they get real defenses. So that stuff the bag of HP just had to eat the Wizard can avoid. As a result the Wizard's HP are effectively much higher and get diminished much less easily. Though just being 2 Con ahead and getting a Blur effect on your person is good enough to make your effective HP the same.
Beatstick boy has 214.5 at level 20 with standard build. Wizard has 151.5. If he has 2 Con higher he has 171.5. Blur means he only gets hit 4 times out of 5, making his HP effectively a quarter higher. 214.375, which would be marginally lower except they both round down to 214.
At level 3 it's 27 vs 15, which becomes 18 after the Con and is effectively 22.5. Though at this point False Life is 8.5, so that would work better.
Not going to illustrate for all the other levels, but suffice it to say that the Wizard matches raw numbers with minimal effort, but is in a much better position to begin with due to not needing to beat monsters in direct stat contests so it doesn't really matter.