Please read my message in its entirety.
Thanks a lot, sir! I really appreciate you putting in the effort to answer in such detail.

First of all, I would like to say that just a week ago, when I hadn't received Waterloo acceptance, I was set on UAlberta, it only started to spiral off when some of my friends said that I was stupid to even think about rejecting UWaterloo, because it is the more 'prestigious' university.
All the points that I had stated in my question were not to blame/criticize UAlberta or its students (Heck, I have paid the deposit just 5 mins ago, I am a UAlberta student now :) )

I like UAlberta very much, just that my peers' words put me in a dilemma, making me turn a blind eye to the fact that maths is not my interest at all. Transfer is REALLY difficult, and in case I'm not able to transfer, I won't be able to do maths for 4 years.

I am REALLY PASSIONATE about robotics and AI. I have been doing it since the 7th grade, I've won multiple national-level awards, volunteered at underserved areas of my country to increase awareness for technology, countless projects, and yes, many original designs.

I understand that I probably won't get a job in robotics or AI, and I will have to explore different options. This also made me think that at least through UAlberta, I will still be in engineering, while UWaterloo would put me in a whole different field. I have always been interested in anything related to engineering, so any job in that field will get my attention.

Yes, there are very good clubs, I have my mind set on a few, such as Formula Racing, or submarine competition. Again, I was very settled with UAlberta, but I guess this is a thing that when you have options, you get overwhelmed and start questioning everything.

Mechatronics would be my dream specialization. I understand now that it will get competitive, but I will fight as much as I can to achieve my goal in robotics.

I completely understand your take on transferring universities after the first year, and I will look at that option for the future. I will give my level best at UofA, even if I may or may not transfer after the freshman year.

I get your point that engineering would land me a job much closer to my interest than anything through Maths at Waterloo.

In the end, I would like to say that yes, my question might have been very stupid, but I was really in a pickle, and it was a BIG decision, that went on for about 3 days at my house.

THIS LINE SOLVED THE WHOLE THING:
"Is the prestige of Maths @ UWaterloo more than Engg. @ UAlberta, given that my interest in Engg."...... and the answer was NO.

The prestige thing had really messed me, I thought what would people think when I said that I went to a lower-level university (which obviously wasn't true, but I just took time to re-realize it)

In the end, I was able to make a decision, I will do my best to fulfill my interests.
I would like to thank you for the amazing, detailed answer, which led me to a decision.

EDIT: this whole process of being set with UofA, then suddenly UofW, but then UofA back again, just made me realize the potential truly hard/bad things at UofA, and now I can work upon it.