For me it would take 12 or 13 years or so for that $1k a day to compound into $7M, and slightly longer if I use some of that to FIRE in the mean time (which i would). If i went for $7M at the start, I would have more than doubled my original winnings with the same 7% return by the 12 year mark. So, if it were me, i'd go $7M, no question. Especially in Canada, no tax on lottery winnings, so no tax benefit to stretching out payments.
I think for most un-mustachians, the $1000 a day might work out better for them, as they weren't going to invest much of it anyway. The un-mustachian winner might do something like this. The $7M payout: Half gets spent right away on a fancy house, cars, toys, boat etc. The remaining $3.5M gets put into a GIC at 3%. The monthly spending to maintain the new fancy house, cars, toys and constant trips, restaurants etc inflates to $25k/month and they run out of money after less than 15 years. On the other hand, if they take the $1k a day (assuming they have a while to live), and spend the same insane $25k/month and put the rest (around $5k/month) into that same GIC at 3%, they end up supporting their crazy lifestyle just fine and have over $1M in savings after the same 15 years.