More Opinion
And some facts.
All the Baltic Birch I've seen over the last few years has 'footballs', oblong-shaped fillers that are used to repair defects in the surface plies. So when I want a good finish I either veneer MDF or buy Hardwood plywood: Walnut, cherry, etc. Most lumber yards don't have it. You have to find the building products wholesaler in your area by asking at cabinet shops. Some of those will order it for you. Good veneering isn't learned in a day and good veneer isn't cheap so the hardwood veneered panels make $$$ sense and save a lot of time.
I recently bought walnut-veneered plywood from China for about 1/2 the price of that from G-P or Weyerhauser, $52 per 4x8 and the quality was very good.
When you buy hardwood plywood also order matching edge-banding 13/16 wide that comes in 250' rolls for about $35. It irons on and covers exposed edges hiding the plies. Of course you hav to figure out which edges will be exposed and tape them before glue up, adjusting the finished size of the box for the thickness of the tape.
Whether you use MDF or plywood there's no reason to use any screws. Screws don't make properly glued joints any stronger. And the torque action of driving them usually moved the panels a bit. You can either clamp w/o fasteners as I do or nail the panels together a la BillFort. Which I also do. It's much easier to fill nail than screw holes. Then cover them with veneer or fill them with color-matched crayons the distributors or most paint stores have. Air nailers and small compressors have become so cheap, and the compressors so useful to have around the house that they've become common. The nail holes from air nailers are much less noticeable than hand nails. Don't bother with 18ga. brads, though, they deflect, especially in MDF. Get the bigger guns that shoot 16 ga. finish nails.
I have no brief on the 'sound' of either MDF or plywood except when it comes to the shelves under equipment. MDF shelves sound hard and etched, solid wood more 'natural'. I've never compared 2 cabinets with the same drivers in both materials and I suspect few others have either. MDF is definitely less durable than plywood as others have stated for cabinets that get moved around a lot. The cheap hardwood plywood sold at home centers is likely to have voids in the interior veneer layers, or worse, loose bits in those layers. The former will show up in veneer eventually, the latter will rattle when you play music.
The Technical Library pages at the JBLPro site has very useful information on cabinet construction and bracing. So do the sites run by Bill Fitzmaurice and Bob Brines. You can find Fitz at the Audio Asylum, if it ever comes back up
Brines addresss is
http://audioroundtable.com/Brines/
You should also visit the American hardwood Plywood site.
Bracing is much more important than the material used. I like what I call 'window pane' braces that brace all 4 sides at once and also help square the cabinet during glue-up:
Cabinets up to 18" tall need at least one brace and larger ones, more. Divide the cabinet unequally to avoid panel harmonics.
There's also a lot of opinion and information on stuffing. I use R-13 fiberglass based on the engineering done by Wayne Parham at Pi Speakers. The very expensive "Black Hole" is supposed to be good as well but why spend the money? All you're trying to do is damp resonances around 50 to 100 Hz which the fiberglas does well. There are worries about airborne particles which may be tamed by using fine mesh over the ports. Keeps the cat out, too. I've never tried it but I used to have info on gluing roofing felt to the insides of the panels that does a good job of dampening. The author used an accelererometer and sensitive measuring equipment to get his results. Can't find the site anymore.
You'll all have to be your own judges in the end.