They both love her, but differently. Prue and Piper were definitely closer and even shared an apartment before moving back to the manor. Piper definitely looked up to Prue, and even more so after discovering the craft--this did stifle her emotional growth because she just ended up seeing herself as the one "who tags along and freezes things". Even after getting her new power she still relied on Prue's emotional comfort and protection (see watermelon vanquish).

In a deleted scene in Hell Hath no Fury Leo tells Piper Prue was trying to protect her and Piper retorted that she didn't need her protection, she needed her to stay alive.