Oh, yeah, there was another thread just like this.
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By concept, different resources have different effects on champions.
Mana for example is a resource amazing at doing a shitton of things at once, sometimes in a continuous stream. Burst mages for example are the prime definition of this as they can often throw at least some spell at a solid pace for long periods of time before dropping their entire kit on the enemy's head. It also provides early game gating and late game freedom, as early game you may have to consistently worry about your mana, but by the later stages of the game you quite frankly do not care about it anymore.
Energy is a resource that, if you are careful about, acts essentially resourceless. You can not fire large amounts of your kit consecutively like a mana user can, but you can drop an entire rotation of spells on the enemy's head after pacing your abilities in a way that your fast energy regen kicks in over time. Energy lacks the ability to build out of this restriction however, so if an energy based kit is designed to max out on energy with only 2 rotations of the champ's spells, you're not going to ever get around it no matter how you build.
Cooldowns, finally, have two significant weaknesses depending on how the champion is built. If it's a champion like Garen who is restricted by longass cooldowns, or on the opposite end of the spectrum Katarina with weak ass spells, resourceless champs are often balanced around the fact that they perform subpar to energy and mana in very specific matchups. Katarina for example is straight up weaker than Talon in many raw damage scenarios if you consider that her ult is easily interrupted and Talon can rely on multiple auto attacks with far more power than the former.
The reason why resourceless champions exist is to put a different spin on a kit than energy or mana could allow. Yasuo's design quite frankly is impossible with mana or energy because his Qs are essentially auto attacks and as his main combat skill damn near mandatory towards his damage potential. Wind Wall was designed as a reactive skill and therefore giving mana or energy is nothing more than a damning limit to using the ability in emergency situations. And don't even get started on trying to make his E function off a resource.