It's been confirmed the bug-catching comp, on top of a Sun Stone for winning and a Shed Skin for not placing, gives you a Sitrus berry for 3rd, and an Everstone for 2nd, akin to GSC.
As for the Game Corner, the minigame runs similar to GSC, but now the top screen features a Smeargle. The prize values for triple Pokeballs or 7's both start at 100, but gradually increases whenever Smeargle shows it is pleased (shows a music note or few when it is)whenever you get 3 in a roll (or the apricorn slot on the left-hand side). Value of triple 7's going up by 4 coins per music note Smeargle gives, and triple Pokeballs by 2 coins.
Whenever you get triple Pokeballs or sevens, a minigame is triggered in which the slots are replaced by pictures of the starters - you have to match them up to get coins, minimum of 20 coins for each instance. Pokeballs has a round of 8, and Sevens a round of 15 of this, as far as I can tell. Sometimes it goes rather fast during this... D= Afterwards it's reset so triple sevens/pokeballs is again worth 100 coins each. Was fun to play.
Prizes include the Pokemon Abra (level 15) at 200 coins, and Ekans/Sandshrew (level 15)depending on the version (Ekans = HG) at 700 coins, and Dratini at 2100 coins (unsure on the level, might also be 15 though, or something around that level). And one of the other prizes is either TM 10 (Hidden Power - idk, a tad unlikely =/), or 10 of some sort of item.