Having these abilities able to be used at a significant discount is important. Cards like Desperate Ritual, Rite of Flame, and Manamorphose suddenly are playable for free! You can create infinite mana with the Ritual and Rite of Flame, since they remain on the stack to copy. With that mana, you just cast Banefire, burning them infinitely for the win.
In fact, Rite of Flame is so powerful in this combo that it’s banned in Modern! Izzet Guildmage Combo was a real deck at one time in the now-defunct Extended format. This is why Wizards was so quick to ban Rite of Flame in the Modern format early on. The combo is still playable in Modern with the other two cards, but the deck now only mostly sees fringe play in Legacy. Talk about a combo enabler!
In Commander, Nivix Guildmage is a tad more versatile, and that first ability is more relevant to filter dead cards out of the hand. Also, like Izzet Guildmage, he can also create infinite mana, but it requires a lot more initial mana investment. The infinite mana combo revolves around Turnabout from Urza's Saga. You use Nivix Guildmage to copy Turnabout, tap all of your lands for mana, and let the copy of Turnabout untap all your lands. Then, keep copying Turnabout without ever letting the original Turnabout resolve. It's similar to the classic High Tide & Palinchron combo, but it's much slower.
Still, Izzet Guildmage is still the far better card here. Nivix Guildmage is still Constructed-playable, but he's nowhere near the efficient combo enabler of his senior associate. He is simply a useful creature that combos well with Manamorphose (which creates two of any colored mana). Having the Blue/Red combination there hurts it with any of the Red mana producing spells besides that one. Sorry, Nivix Guildmage, but you don’t stand a chance in this match-up.
Winner: Izzet Guildmage, for single-handedly making Rite of Flame banned in Modern.