Two satellite are at different height (smaller and larger) from the surface of Earth. Which would have greater velocity?

I suppose that both satellites have circle orbits, not general elliptic. In this case their speeds are constants throughout entire path around Earth.

In this partial case Kepler's Third law states that for different (small) bodies orbiting the same planet (Earth in our problem) the expression `P^2/a^3` has the same value. Here `P` is an orbital period of a body and `a` is a distance from a planet's center. Speed is obviously `(2 pi a)/P.`

Therefore `P_1^2/a_1^3 = P_2^2/a_2^3,`  or  `P_2/P_1=(a_2/a_1)^(3/2).`  Speeds are `V_1=(2 pi a_1)/P_1`  and  `V_2=(2 pi a_2)/P_2,`  and

`V_1/V_2 = (a_1/P_1)/(a_2/P_2)=a_1/a_2*P_2/P_1 = a_1/a_2*(a_2/a_1)^(3/2) = (a_1/a_2)^(-1/2).`

So if  `a_1gta_2,` then `V_1<V_2.`

The answer we obtained is: the more the satellite's distance from Earth's surface (and therefore from Earth's center), the less its speed. Although period is still greater for a more distant satellite.