I've had the same thought. I feel it's the pacing and Pike's general behaviour making me think of Picard. Of course thats only because we've had TNG. Before TNG I'd have just said The Cage just feels different but with no real comparative reference.However, is it just me or does The Cage feel more like a TNG episode than a TOS episode? It doers to me anyway.
As you know the studios thought the Cage was to cerebral so they changed TOS. I have always thought that TNG seemed truer to what Gene originally envisioned Star Trek to be without a studio dictating to him.