Haven't heard of a p-q frame before. I suppose you mean alpha-beta frame. Ok, so assuming it's a question on alpha-beta and d-q frames, here's my two bucks:
alpha-beta is a stationary frame. We know that the AC side voltage/current pulsates at 60Hz. Hence, if you describe your current phasor in alpha-beta coordinates, you'll notice that the alpha-beta components of your current is time-varying (even though you have a constant amplitude current). The current phasor is described by i = i_0 exp(j(wt+phi)), where i_alpha = i_0 cos(wt+phi) and i_beta = i_0 sin(wt+phi). If you are designing your controllers in alpha-beta coordinates, you must design a reference tracking controller at 60Hz.
On the other hand, d-q is a rotating coordinate system and rotates at w = 60Hz. Thus the quantities described in d-q coordinates are fixed (constant) for a constant amplitude signal. d-q gives you an advantage to design controllers for low-frequency tracking (since the quantities are described as DC quantities in this frame). However, this comes at a constant of synchronizing your d-q reference frame with the AC frequency. This requires additional techniques such as PLL.