What are the pros and cons of having canard control surfaces versus a horizontal tail control surface?
For statically stable aircraft, the canard is a spoiler in disguise. It will create a strong downwash right behind itself, coupled with an upwash outward of $\pi$/4 of its semispan. With changing angle of attack and lift coefficient, the vertical position and the strength of both up- and downwash will change, so the wing incidence variation over wingspan can be made right for just one angle of attack.

Pros


The force to effect flight path changes works the right way, so pitch response times of canards are slightly better than those of a conventional configuration.
The wing can be further aft, so in short business jets the cabin might not interfere with the wing spar.


Cons


The induced drag at off-design points is higher than that of a comparable conventional configuration.
The bigger lifting surface must keep some stall margin, so the total lift coefficient will be smaller than that of a comparable conventional configuration. In the end, a canard will need more wing area.
Control surface deflections will add to the already high lift coefficient of the canard plane, increasing lift demands on the surface with the smallest margins.
The highest lift coefficient is needed at the surface with the smaller Reynolds number. Normally, the reverse would be better.
If the engines are mounted below and ahead of the wing, they will be hit by the wake of the canard, reducing intake efficiency and compressor stall margins.
To make sure that the control surface will be the last thing on the plane to run into compressibility problems, it should have less lift coefficient and more sweep than the wing. In the end, a statically stable canard will have a lower cruise Mach number than a comparable conventional configuration.
The landing gear must be made to retract into the fuselage, because the wing is too far behind the center of gravity to allow the gear to retract into the wing.


I could go on, but I guess you see by now where this is heading …