Does Uranus have a stronger gravitational pull on its moons than Earth does? I've read that Uranus has a lower surface gravity due to its lower density than Earth. However, does this mean Uranus has a weaker pull on its moons than Earth does for the same reason?
The "strength of gravity" (ie gravitational acceleration) is determined by the mass of the planet and the distance between the planet and the moon. The formula is 
$$GM/r^2.$$

For the Earth (mass= 1 Earth, distance to moon=390000km) the acceleration is $0.003 ms^{-2}$
For Uranus and Titania  (mass =14.5 Earth, distance=435000km) the acceleration is $0.03 ms^{-2}$

In summary, the gravitational pull of Uranus on its moon Titania is 10 times greater than the gravitational pull of Earth on her moon.

The same formula applies to surface gravity:

For the Earth, (mass = 1, radius = 6370km) the acceleration due to gravity on the surface is $9.8 ms^{-2}$
For Uranus (mass =14.5 Earths, radius = 25400km) the acceleration due to gravity is $9.0ms^{-2}$. 

The surface gravity on Uranus is less that that of Earth, due mostly to the relatively low density of Uranus meaning that you are much further from the centre of the planet when you are at the surface.

(These value vary due to the neither the Earth nor Uranus being perfectly spherical, and the effective gravity is also lower due to centrifugal effects)