'Professional' usually refers to the TOTL. Probably more a cost description than capabilities. After all, if you use the term for the MOTL and below, what term do you use for the TOTL? 'maestro'? 'Upper Management'? 'Superstar'? LOL
One 'professional' feature missing conspicuously from the PSR series is a sampler.
Then there is build quality. Something that USED to mean something until we all got too frail to lift a well built piece of kit!
I think that I tend to agree that the Korg's lead sounds, particularly the SA (DNC) type ones still have a ways to go to equal Yamaha. But, OTOH, their arranger sound, particularly how punchy and live the drums sound (without needing backing tracks!) leaves the Yamaha PSR's in the dust. I guess it depends on your priorities. Me, I figure I can probably finagle a less than stellar lead sound to sound good simply by what I play on it. But if the rhythm section don't groove, don't sound like they are live, not much I can do about THAT!
I have to confess, the more I read about the PA600, the more I am impressed, particularly at the price. I could care less about a harmonizer (and if I did care, I'd be using a VoiceLive or something that sounds good, not the wanky ones built in to most arrangers), and at considerably less than a PSR, this seems like quite the deal.
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An arranger is just a tool. What matters is what you build with it..!