Which is more organized and easier without requiring tons of moving things around and organizing?
Depends ...
If you do want to move things aroung a lot ...
Hotbar is more organized, since you are the one who is sorting things the way you want ... if you do, and also you want to use "pops up special abilities window" ... bad luck for you, things are allready sorted the way developers want them and you cannot move with anythng. :P
If you do not want to move things around a lot ...
They are just the same, bcs things can easily be sorted in same order as they was in "pops up special abilities window" ...
And the only differente here is that they are on single bar, instead of two separate bars. -_-
And if you principialy refuse to move things around no matter what ...
Then, and only then, "pops up special abilities window" can seem better ... bcs you are too lazy/stubborn/whatever to keep maintained your hotbar, but that is, once again, not faut of that hotbar.

1. Slot 1 = Sneak Attack Ranged, Slot 2 = Throw Brine Shell, Slot 3 = Cunning Action Dash, Slot 4 = Sneak Attack Melee, Slot 5 = Potion of Speed, Slot 6 = Lesser Healing Potion
2. Button/Hotkey pops up Special Abilities window where Sneak Attack Melee and Sneak Attack Ranged are listed one after the other, Cunning Action Dash is there also, Button/Hotkey pops up Spell list window with all spells by spell slot, Button/Hotkey pops up window with Item list such as potions and throwing objects in order as they are in inventory
Also, there is second question that should be asked ...
What does work more smoothly? :P
1. Slot 1 Sneak Attack ... see > click > aim > cast
2. Button/hotkey pop up ... open > search > see > click > aim > cast
I believe someone allready counted this with some buff spell ... not sure wich it was tho :-/ ... in debate about old (every spell level had own icon) vs. new (popup window with spell levels) casting system.
It was a little different topic, but i believe the same example can be used here too:
Lets say you have 4 Wizards party and you want to cast Mage Armor to each ...
Hotbar:
1. Wizard ... Click on icon > cast
2. Wizard ... Click on icon > cast
3. Wizard ... Click on icon > cast
4. Wizard ... Click on icon > cast
That takes 8 clicks to buff them (11 if you count switching characters)
Pop-up:
1. Wizard ... Click on icon > pick level > click again > cast
2. Wizard ... Click on icon > pick level > click again > cast
3. Wizard ... Click on icon > pick level > click again > cast
4. Wizard ... Click on icon > pick level > click again > cast
That takes 12 clicks to buff them (15 if you count switching characters)
(The original example was about something else tho ... but i didnt find it.)