Hi.
Unfortunately the reality of it is that no-one really can tell You -or to anyone else for that matter- that.
The main reason for that being the fact that there’s a gazillion ways to manufacture either MDF or plywood, and up until recently the materials ability to be cut -or marked- with visible wavelength laser haven’t even been on the list of properties to aim for.
So all the materials sold under those two looseish marketing terms have been engineered and manufactured with entirely different goals in mind.
While in theory MDF would be easier or at least somewhat more predictable to cut than plywood since the material is more homogenous by nature, the bonding resin that ties those medium density fibers together throws a huge wrench onto that theory in the real world.
So, we basically have three choices.
From the cheapest to the most expensive.
The cheapest is to cut what ever we can find cheaply or free, and don’t mind lots of trial and error, a bit of charring, occasional fires and occasionally ruined work.
Those tendencies can be greatly reduced if the cutting is performed in an inert (nitrogen if on a budget) atmosphere.
The next is to do extensive research on different moderately priced MDF and plywood varities to find the exact one that’s easiest to cut.
The problem is that one usually has to buy the whole ~2.5m2 sheet, not just small pieces to test on.
And when we eventually do find the least problematic material, keep our fingers crossed that the next sheet is actually manufactured with the same materials and in the same way.
The third is the easiest and also by far the most expensive, to buy either of those materials as “laser approved” stock.
Keeping in mind that not all the vendors are necessarily completely honest with their marketing claims and strategies 
.
Up to 10 times the price for putting a “laser approved” stamp on regular plywood may prove to be next to impossible to resist.
With plywood there is a fourth rather marginal choice for the HC DIYers, rollin’ Your own.
There’s a recent thread about that, I’ll edit a link to that when I find it.
EDIT:
With the plies of the exact species of wood we want (or can find 
), grain oriented the exact way we want, and the exact choice of natural glue to bond those plies together, we can engineer the optimal plywood to be cut with our visible spectrum lasers.
Keeping in mind that most of those natural glues are animal based, while on the regular plywood the glue (and the in MDF the bonding agent) is most likely (semi)synthetic or petroleum based, often some sort of formaldehyde mix.
Even though it is in theory possible to make MDF the DIY way and to engineer it to be more laser cut friendly, I for one can’t figure out why on earth would someone wish to do so.
I do hate that recycled wasteproduct with a passion.
But that’s probably just me.
Regards,
Sam