Its not clear from your comments whether you are saying the styles sound different, or respond differently. I have a 605 and have played the 709 and not noticed any difference in the way the styles respond to fingering or chords, between the two, or for that matter the Tyros or PSR range going back many models. So not sure what you are experiencing, but I don't think it should 'play' differently. Yes, it may 'sound' different because there have been voice, style and sound system upgrades, but they are not drastic.
If you think it responds differently to your playing, then maybe you need to check that you have set up the fingering and split points to suit the way you play. I am not familiar with the 509, but it is possible that more set up options were introduced in the 709 than available on the earlier model, and you need to go through that. Its pretty straightforward to do this using the touch screen, but the actual settings you want depend on how you play i.e. full keyboard, split keyboard, full fingered, fingered on bass etc.