I learned to play on both piano and organ keyboards, and both have their advantages. There is a difference, but just because you learn to play keyboard on one type of keyboard does not mean that you cannot learn techniques to playing on the other type, as well.
I usually prefer the organ/synth action keys, as long as they are of at least a decent quality, as the light touch does make fast playing easier, and it also makes it easier to play multi-note chords with one hand.
However, a hammer-action weighted piano keyboard does, in my opinion, allow for more expression -- even when compared to a velocity-sensitive synth-type keyboard. If I was playing a gig that mainly called for piano music, I would likely use my 88-key weighted board, not my synth-action PSE-E433.
But again, there's no reason you cannot learn both. Maybe not at the same time, if owning both types of keyboards at once is not feasible. But eventually. For now, as previously suggested, decide what you prefer most, such as by visiting a music store with both types of keyboards and playing both. Also factor in what type of music you are wanting to play. If it's piano-based, then that will edge you more toward weighted keys. If it's more synth-oriented or multi-instrument arranger-style music, then that would likely edge you more toward the organ/synth-type keys. But of course, there are keyboards with arranger-type features and weighted keys, such as the better Yamaha DGX boards.
I've played around with a PSR-E463 recently at a music store, and I've previously played around with the E453 when it was a current model, and while I agree that the key feel is not as good as my older E433, I personally wouldn't say it is so bad that it would hinder development of learning to play a synth-style keyboard.
EDIT: I took another look at the original post and saw the part about finding it difficult to jump from key to key instantly. That just takes practice, regardless of the type of keyboard you're using. Yes, a really flimsy keyboard might make this more difficult, but I don't think any modern keyboard from Yamaha today is that flimsy. I would just avoid something with mini-keys, because the difference in the actual size of the keys does make a significant difference when playing a song. But to reiterate what I said above, I really don't think it needs to be an either/or situation with learning to play a synth-type keyboard or a weighted piano-type keyboard. You can learn both, and you can learn them together or in whichever order you choose.