With the keyboard volume at zero they feel (and sound) identical. Casio does seem to describe them differently, but I believe they are mechanically the same. Where the PX-S3000 shines is with its piano sounds and the responsiveness due to the software that translates what you play to the internal sounds. The difference is remarkable and changes the way it feels when you play. I don't feel or hear a difference when using either as a MIDI controller with Logic. The PX-S3000 can be set to transmit High-Resolution MIDI, but the CDP-S350 does not. I've done very brief experiments with HR-MIDI and PianoTeq, but I haven't formed an opinion yet.
Other differences are that the speakers in the PX sound better, and it has 2 very useful controller knobs which are semi-programmable. Another plus of the 3000 is that you can control the balance of sounds in layers and splits. The lack of layer/split balance is is a real shortcoming and a deal-breaker for me with the CDP-S350 as a gig keyboard. If splits and layers are important to you, you should skip the CDP-S350 and go right for the PX-S3000. The CDP-S350 is otherwise a great value and a really fun instrument to play. Both keyboards seem to have the same selection of rhythms, and I agree with @Joe Muscara that they are easier to navigate on the CDP-S350. I love the data wheel on the CDP and wish the the PX had one. Surprisingly, the CDP-S350 can import new rhythms, but the PX-S3000 can't.