I can't speak for every make and model on the planet, but you'll have to do your own legwork comparing specs on the individual models you're interested in.
Depending on the individual manufacturer and model there are varying levels of tweakability.
Features to look for are splits and layers, the number of user slots available as "registrations" or "setups" or "user voices" as well as sampling (expensive on most boards) and envelope and filter tweakability (generally under FX sections) as well as on board sequencing if you find it necessary to run backing tracks and a step sequencer if you are into modern drum and bass music to name just a few.
Take a closer look at the Casio PX-5S and the PX-560 videos on youtube to see the programmability of these units. I can't really speak as to the programmability of the DGX-660 as I'm not a big lover of Yamaha.
Also worth considering is the level of support you'll find online for your board. I used to own a Korg TR76 and online support was essentially zilch.
Another feature worth looking at is availability of a computerized patch editor or do you have to make all your edits on the keyboard itself? Are third party patches readily available? Are they free or do you have to buy them?
Do you need accompaniment or backing tracks? Are you looking at workstations or arrangers or stage pianos? Do you want to work only with Synth sounds or do you need "bread and butter" sounds as well? (pianos, organs, strings, orchestral, etc?)
Personally if I needed to replace my Kurzweil Workstation these days I'd be looking at the Roland FA-08 or the Casio PX-5S or PX-560, but some of these are all almost double your stated budget.
Also don't forget you can use any decent MIDI keyboard as a computer MIDI controller as well so you can also use them with hardware modules and computer VST virtual Instruments to infinitely expand your range of sounds.
There is no perfect keyboard available at any price on today's market but what it boils down to is defining your needs and comparing specs and prices wisely in order to arrive at the best compromise for your budget.
Gary