There is a two questions regarding thu'um that has been bothering me.

Firstly, since all dragons, including Alduin, who is the son/another aspect of Akatosh, use thu'um as their primary weapon during combat. Does that means Akatosh use thu'um most of the time as well?

Secondly, is the nature ability to use thu'um the main reason that the last dragonborn is that powerful or does having the dragon soul gave him more power than that?

On the side note, regarding how powerful the last dragonborn is. Since the Alduin you defeat is a weaken version and we have no idea how powerful Miraak is when compared to other higher being. The only material I can use to judge how TLDB is where clavicus vile claimed that you are at half his power, so I assume the max power TLDB can reach throughout the course of the game is half as strong as a daedric prince.

An avatar of Akatosh would use the thu'um, but the actual Akatosh couldn't shout as he is half-dead and his body takes the form of the planet Akatosh that can be seen from Nirn floating in Oblivion.

All dragons are a sort of aspect of the Time Dragon as their souls broke off from him at the beginning of time, though the Last Dragonborn is more recent. Some are just greater aspects than others.

Everyone has the natural ability to learn the thu'um, but it takes years of practice to learn even a single word of a shout, while the Dragonborn can learn it in a single day. Having a dragon soul is what allows the Dragonborn to learn shouts quickly like a normal dragon, as it allows them to absorb the knowledge from other dragons. Having a dragon's soul which grants them the ability to absorb the souls of other dragons is what makes them powerful.

Regarding power, there is this quote from Neloth:

The most powerful would be Tiber Septim because he became a god, but it would still make you more powerful than Miraak according to Neloth, which I suppose you are since you do defeat him.