controllers evolution

Well, you will have to mount the Sevcon Gen4 controller on some large piece of aluminum sheet metal in order to dissipate the heat. The Sevcons tend to supply a "BLDC" motor with sine-like commutation currents, so they should be a little more efficient than the ususal noisy Chinese controllers with rectangular commutation current.
However, Kelly have such powerful controllers too nowadays. You just need to pick it one class higher than you might assume as they heavily restrict maximum power and startup current to ensure thermal health of their MOSFETs.

I am not sure why you did not read on, as I continued with Kelly having more powerful controllers nowadays too :-)
And believe it or not, your motor IS an AC motor, a synchronous permanent magnet motor to be exact. It can be powered by definition like a BLDC motor with trapeziod commutation (like a Kelly) which is noisy, a little choppy at low speeds and slightly less efficient, or it can be commutated with AC current which is smoother and slightly more efficient, like with said Sevcon.
Check out this website, move your mouse over "BLDC motors" and click on "Block star" to see approximately what a Kelly KEB for example does with your hub motor. You change RPM and rotation direction with a slider at the bottom of the animation window. You will see that motor operation is rather choppy at slow RPM.
Next move your mouse over "BLDC motors" again and click on "Block sinus" to see approximately what a Sevcon Gen4 does with your very same hub motor. You will see a very smooth operation from standstill, though at high RPM things will look similar to what the trapezoid commutation does.

From a practical perspective Kelly are a lot better for DIY folks, and will probably supply you with the most bang for your bucks. But make sure you choose your controller at least one size bigger than what you may assume to need.

As a Kelly seems to have worked with your XM4500 I am led to assume it did not originate with Efun with it's 6-phase motors, but that it has a standard 3-phase motor? Only then would a Sevcon Gen 4 also work.
My first question is about your battery voltage: is 69V the shut-off voltage at the end of charging, or is it the standard voltage of 21 LiFePO4 cells? Because you will have to choose a controller where maximum operating voltage is above that maximum end-of-charge voltage. In the case of the Sevcon G4827 that maximum voltage is only 69.6V. Above that it will most likely shut down and refuse to operate. And as you want to add another cell the G4827 would be completely outside it's specification.
The G8018 on the other hand has enough voltage headroom, but maximum continuous current is just 75A. Is 80A a continuous current in your scooter? G8018 could not handle that for very long.
And you need to know what you are doing if you plan on one of the Sevcons. You will need extensive knowledge of the connector pins and have a fitting connector to change your wiring harness to. Plus you will need access to a Sevcon programming unit to fine-tune the controller to your needs. But it should indeed be rather quiet compared to a classic Kelly controller.

On the other hand, as you already have a Kelly on board a slightly more powerful Kelly controller model will be a plug and play solution with not much to worry about, except maybe programming some current limits so as not to fry your motor nor it's leads. And possibly activate the option "Noise Reduction" in step 3 of the programming, as the noise is bothering you too. But do not forget that some noise can be helpful to give pedestrians that only use their ears instead of eyes for navigating roads and driveways better warning that you are close by :-)

c) I notice that You have a Kelly KEB72801X, and I looked at all Kelly Products and I feel lost because there are so many

my last questions are :

?1) what is the real subjective difference between these controllers? till now I understand the Noise, I read that sinus controllers have 5% more torque, but do you feel it?

?2) changing your controller did you had a real better feeling or afterall it was not so different from the old one?

thanks - renato

c) Kelly is actually pretty well organized, but they DO have a LOT of variants and products :-) As you are out for a controller first click on the Products icon, and the first page to pop up should already be the "Controller" one. What should help you for a first shot is to understand the way Kelly name their controllers:
The class of controller is defined by the letters: KEB stands for Kelly E-Bike and is pretty much exactly what we need for our electric steeds.
The first two numbers give you the nominal maximum voltage that the controller can be used for. In your case, and in particular with your additional cell, you should look at the controllers starting in KEB72, not KEB48.
The next two numbers state the maximum electric power output in kW x 10. Now remember this is the electrical power, not the mechanical power that your motor is capable of. If the 4500 in your scooter's naming refers to a mechancial power of 4.5kW and you take into account that it's maximum efficiency might be in the region of 88%, you will realize that you need to look for a controller that outputs at least 5.1kW. So the minimum Kelly to look for would start in KEB7251. But alas, the next bigger one is already a KEB7260. So what! :-)
The last digit is 0 or 1, the latter means the controller has the feature of regeneration, and 0 thus without regen. There is a 50US$ premium for the 1, so you have to know if it is worth that much to you.
KBL Controllers additionally have the ability to speak CAN, but that will not be necessary for you and also costs more. KBL naming is slightly different in the third and fourth number which gives the absolute maximum motor current that can be output in very rare instances, in A / 10. It is better to look for a KBL with double the number you are looking for, which in your case would be 80*2/10 = KBL72160 or KBL72161. The website only lists the KBL72151, which would be slightly less than what you are looking for. Fitting would be the orignal controller in my bike which was the KBL72201.
But as I wrote, if you have no dealings with CAN bus stick with KEB.

?1) As I only have personal experience with Kelly so far I can only judge from youtube videos what the noise differecne is between a Kelly and a Sevcon Gen4. To be very honest, even the Sevcon makes a similar humming noise to the Kelly in our type of Erider motor, though it appears to contain far less high frequency content and thus is more of a hum instead of all sorts of weird creaking sounds at low RPM. But that is only when the microphone is aimed directly at the motor. When riding that hum is not really audible. But as to performance, in the end it is current that decides over sluggish or spirited performance. Which brings us to

?2) The orignal KBL72201 in my 5/8kW Erider Thunder was cursed with VERY weak stall and low speed current in the order of well below 20A, and there is NOTHING that can done about that with normal programming. That controller is very simply to weak for the motor. The KEB72801X we had to limit quite severly to ensure that maximum current would stay in the same 150ish A range as with the orignal controller. That was in a speed range of about 25 to 55km/h, and the bike takes off like there is no tomorrow in that speed range. But with the orginal controller I was always ashamed when I was first in line at a red light, because takeoff from standstill was such a drag... And on even pretty shallow uphill gradients I had to push-start the scooter in order to get it going and get over the extreme startup limitation. THAT has been cured completely with the KEB72801X, despite the programmed limitations. I can now easily start going on the 21% slope up to my dealer's garage, AND accelerate up there to 30km/h and more. But the motor leads do quickly heat up during such extreme use, which thankfully is not really a problem because there are not that many 21% grades around :-) Normal level road acceleration is completely harmonious and POWERFUL from standstill up till about 60km/h now, were before it felt like barely starting to move, and above 25km/h a sudden kick in the butt and off it went. That works from standstill now, if I want it to :-) If not I still have the wonderfully gentle control over motor torque that the Kelly's allow with gentle use of the throttle, which I REALLY need when having to ride on icy roads, like probably tomorrow morning again.
So a wholehearted YES, I do feel a BIG performance difference, yet my charging energy use over distance travelled has rather slightly decreased despite the more spirited ride. I assume this may come from less thermal loss in the bigger MOSFETs of the upgraded controller.

usually, a controller should have a temperature sensor inside, which will shut off the power when the controller is too hot.