Because the Queen is a figurehead of State, she's Head of State, but not head of government. The Queen receives state money from our elected government to perform her duties as constitutional monarch, but she also owns stuff and buys stuff in a private capacity. That is a very real distinction because our monarch is not both government and Head of State
The Sheikh's brother is Head of State and head of government.
Sheikh Mansour and his extended family is the government of the UAE, he is a high ranking member of an absolute monarchy with exclusive executive and legislative power. From what I've read he's a smart well educated man and makes decisions regarding the sovereign wealth fund in a responsible way. Besides I'm sure there are checks and balances in the system that prevent him from splurging the investment fund money on fast cars, villas and yachts should the fancy take him.
That's not to say the Sheikh doesn't spend money on fast cars, villas and yachts, he does, a lot of money, but he does that in a personal capacity, but when he does spend his own money, he just takes one hat off and puts on another, because he is the living embodiment of both the State and the Government by dint of birth, in a way the Queen is not.
In a nutshell our detractors, the Guadianista's and Simon Jordan's are bad faith actors, they see the ruling families of the Gulf as nothing more than gangsters, hoarding the countries wealth for themselves, they have no respect for Sheikh Mansour because they have no respect for the "rigged" system that keeps him in power.
They point at Sheikh Mansour and accuse him of spending State money because he is the State and consequently all his money is State money. The difference between state expenditure and private expenditure, which is very real on the ground in the UAE, cuts no ice with them, they see it as a contrivance, it's all the same money they shout, just in different labelled pots, and while there are holes in this analysis, there is enough of a grain of truth to it to make comparisons with a constitutional monarch, like the Queen, look ludicrous.