Maybe order and pace are the wrong words to use, but I think you know what I mean. You don't have the same dynamic where the fighter can go all day using all their power all the time meanwhile the wizard holds back and then bursts out with power.
It's a thing in a lot of games because it affects how a character feels to play. I don't know If I can really put this into words. How you gain power impacts how you play a character. Imagine a wizard who recharged their spells by drinking. They would play way different then a wizard who recharged their spells by sleeping.
This is worth sitting with. I love the balance that 4e brought to the pacing of characters (destroyed the Linear Fighter, Quadratic Wizard of previous editions), but I do agree that there's something unique and fun about how in 5e each class has its own pace of growth. I think 5e did a lot to make those growths balanced despite the difference in daily pacing, and that it ONLY works if you can avoid the 5MWD and stick more or less to 6-8 encounters a day, 2 short rests, and a long rest between days (changes in the rest and encounter pacing mechanics of any time will have ramifications that ripple through the entire game. You can make those changes, and the 5e DMG advises on that, but those ripples might flip the unbalance game on its head to make Marathon Fighters, Sideline Wizards). 4e resolved the balance issue elegantly, but removed the class characteristic pacing that nomotog speaks to.
Of course, that requires buying into the pacing narratives of D&D. If you don't think D&D should have specific narratives for Fighters who "can do this all day," while Wizards go nova and want to rest, then 5e's pacing doesn't quite match what you want, and maybe then 4e suits your narrative desires. 5e's different paces could actually be a restraint narratively – why do Warlocks get to recharge their spells every short rest while Wizards use it and lose it? We have to buy into the story being told through the mechanics, and hopefully it's a good story.
4e (before PH3 and Essentials*) did something different from all the other editions. Therefore FrogReaver has a point about it being different: Everyone has the same basic class pacing mechanic for their most prominent abilities. Adrac also has a point – 4e has far more similarities with every other edition of D&D than it does to any other game (13th Age notwithstanding; I'd personally say 13A and PF count as competing IP but still D&D). I find the argument above a bit obtuse and both sides are calling bad faith on each other, when they both are right, from a certain point of view.
**By 2010, WotC was already trying to mix it up and show how the edition could handle mechanical pacing more similar to other editions and breaking from the PH1-PH2 mold. There really good arguments made above in service of both sides of this same-yness argument regarding the shift that occurred with PH3, Dark Sun, and Essentials.
Me personally, I see these as attempts to create a 5e within the 4e framework, and was frustrated by square peg round hole (these would have been great options to include from the start, but felt bolted onto a different system). But I felt they didn't upset the balance, just assumed a new balance (everyone should get a Heroic Theme, for example, which means 1st level is now more similar to what 3rd level used to be!). I was happier, then, to see Clerics adopt the Warpriest Domains from the get-go in 5e. I still think 5e could do with a similar backward attempt to dial up the combat game to feel more like 4e if we so choose, but perhaps that's best left for a hypothetical 6e.
EDIT, Addendum: I also have a close friend who DESPISED the 2010 changes to 4e, because it threw off that pacing balance that made the game work for him just perfectly and never had to worry about different characters pacing differently. He also very much dislikes 5e (not surprisingly). So when we talk about 4e, we do have to talk about 2008-2009 4e versus 2010-2013 4e, as they have significant differences even if they can mesh together into one game. It's akin to past edition revisions: I can and did take 3.0 Oriental Adventures and add the classes and races into our 3.5e games, but I was VERY happy for the reworked mechanics of those characters in the 3.5e Complete series.
When major revisions or changes in directions affect an edition, we do need to discuss that, because it serves arguments for both (4e is all the same!) and (4e is not all the same!). There are different arguments to be made regarding each portion of the edition, and not dialing to reflect that shift does affect the debates of this thread. As for my friend and I, we're not going agree on these things, but I do see where he's coming from. 5e does not have the dials to make it the game he enjoys playing. That's a real shame.