I find it amusing to be discussing mdf or plywood as defining "high end"..
JeffD is right on with his viewpoints on the use of plywood and why it should not be considered for this project - I'm assuming we are talking about doors here, correct?
In my experience - poplar core is the least desirable for any panel that necessitates the need for flatness (ie: a door vs a secured end panel). Poplar just moves way too much (imho).
As to screws holding in mdf - I am assuming since it's a "high end" project, European style hinges would not be employed - but rather quality mortised butt hinges, (not those cheesy "no-mortise" do-it-yourself garage shop type). So - we are talking screws into end grain of the mdf as opposed to the Euro style hinges that utilize screws into the face(back?) of the panel. A small bit of epoxy squeezed into each pre-drilled hinge hole before inserting your screws will give it a bit more holding power and lessen the chances of them loosening down the road.
Guess the term "high end" is recognized differently from one shop to another. I smile whenever I see frameless kitchen cabinets (fabricated with flake core melamine boxes) advertised as "high end", usually with outsourced solid wood pre-finished doors and lots of gaudy moldings, purchased cnc carved and face applied onlays, capitals and corbels splattered endlessly all over the place.. I guess it's just the purist in me. Not that I have anything against frameless construction, but I wonder if pricing is now the gauge to measure the distinction between "high" and "low" end cabinetry rather than construction methods, materials and applications of joinery...
Not looking for a war here. Just expressing the opinion of a sixty two year old who has come through the ranks since age twelve.
My advising answer to the OP - I say go with the MDF (double refined at the minimum). Your customer will be remarkably silent about any warping as that is your best chance of not having it in the first place! :-) And given the veneer you selected and the time and labor involved to apply I don't see the core selection as any issue the homeowner would be concerned about as this is in no way a cheap job... The main issue should be worrying about the longevity of flatness of your doors - that's what his discerning eye will see - not the core.