What are the benefits of legendary skills?

I got pretty much all of my skills to level 100 on Skyrim, and now, I have the option to make them legendary.

I searched on the wiki and found that this will reset my level to the initial value i.e. 15.

I have also downloaded the skyrim community unlocker mod, which increases the level cap from 100.

So, my questions shortens to- Is it beneficial to turn a skill legendary and get all your perk points back, or continue with leveling up with the help of the aforementioned mod I have installed?

I want to level up fast (The character level), so which one of the above would help achieve my goal with better efficiency? Also, are there any special items you get once you make all your skills legendary?

Making skills legendary should be faster, unless the mod messes with the skill gain rates. If it takes you longer to get from 100 to 101 than 15 to 16, then legendary is the way to go.

The fastest, by far, skill to make legendary is Illusion. Getting to skill 90 is fairly fast with Muffle.

Casting Harmony in Whiterun will go from level 15 to about 55. 8 casts with the right bonuses (Well Rested, Mage Stone) will make it 100 again, and that will be about 2-3 levels.

As for the second question, legendary skills don't do anything other than letting you level it again, to gain more character levels.

The net benefit in the end is more magicka/health/stamina, because you'll have to choose either one when leveling up. Depending on your game-play style, this could increase the fun.

Spells you once learned, will always stay learned. When making a magicka depended skill legendary, you'll notice that spells will take more magicka to cast. If you are a higher level with, say, 600 magicka, you will be able to cast high end spells on a low skill level.