Sorry I'm late.
50:50 if not 45:55 DK.
We've already gone over the obvious stuff like DK's weight, KO power, and gimpable recovery, so I'll just go ahead into specifics.
Cape ***** DK close to worst in the game onstage. Reason being that cape is safe on shield meaning capejump to bait shieldgrabs, shield pokes, DK has no disjointed hitboxes so it outprioritizes his everything, AND he has alot of dedicated attacks. Use it whenever you feel vulnerable or you predict an attack. It'll work wonders. Don't be afraid to pivot backwards while grounded.
Fireballs are your best friend for approaching (if you plan to approach) so keep them handy. Don't be afraid to lob them offstage before you come in for a cape gimp if you're trying to force an upB out of him. Speaking of which, DK's recovery is easily gimped by cape, BUT DK can just as easily recover high to protect himself. If you can manage it, Fair meteor works well on DK because of his short vertical recovery. DK also has an insane momentum cancel with upB that works as well as G&W's, but leaves him in a freefall afterwards. Punish this at any cost. Cape will certainly do the trick. DK's upB is ridiculously amazing on the ledge. The invincibility frames on startup and the initial knockback give it the ability to easily beat our upB and allows him to auto-regrab the ledge. For this reason, I wouldn't recommend capeglide vs DK since he could easily grab the ledge before you get to return. Try your best to stay out of this situation; there aren't many options for you here.
Unless you're on a stage with a low ceiling, don't bother saving your Usmash. Like A2 already said, it is amazing in this matchup because of its priority and where it puts DK above your head. Just don't forget that your Utilt is also great for getting DK above you for combos. Grabbing is essential in this matchup as well, since DK's not safe to attack on shield. Stay unpredictable because DK's grab range >>> yours, so grabbing from the front is only safe if you're faster grabbing than he is.
If you're in KO range, remember than DK's safest KO move is Utilt (unstale). It's quick and kills at around 110% IIRC. Next is Uair, which makes capestalling above him ridiculously unsafe because of how high he jumps. This alone is why I think BF isn't as good as it normally is for Mario in this particular matchup. Dsmash usually follows the novice DK's spotdodge, but a seasoned one will often use the initial hit of Dsmash (while DK has his arms above his head) to kill. Generally around 110% is where you'll find this killing, and it's the most likely to be unstale since it's the least safe. DK's Fsmash can kill at stupid low percentages, so don't get hit by it; it could cost the entire match.
More to come...
Edit: DK can cargo spike at higher % if you don't mash out quick enough, but under 100%, you can easily escape it by holding up on the control stick when he grabs you. You'll break out every time. This requires no timing or anything. Once he's grabbed you, just hold up until you're out.
While platforms give him about as much of an advantage as they give us, I'd probably still go BF since we can keep pressure well here, and DASS (dash attack stage spike) works on its ledges. FD I personally wouldn't try because of how easily he could wall us with Bairs there. I can't think of a stage that gives us a huge advantage though.
Overall, I'm thinking 50:50 or slight advantage DK because he completely outranges Mario, kills much faster, and can wall very well with his Bair to keep Mario from getting in constantly. Once he's got his momentum, it's hard to stop him. If the Mario is adept at comboing and gimping however, DK is in trouble because approaching DK isn't all that difficult even with Bair.
In the event that you live in an area that still hasn't realized how bad Luigis is and you're forced to play DK here, keep one half of the mansion destroyed at all costs and camp on that side. If DK has to approach you, the threat of his downB is gone until he's successfully gotten within your range. Don't forget to jab lock either.
