"Let's start by considering the format as it was BEFORE BNG. We have Mono B Devotion, Mono U Devotion and UW Control as the best decks. These decks beat traditional red aggro in the following ways:
Mono B: actually doesn't. Had traditionally had trouble with swarm decks. Particularly weak to Young Pyromancer and Chandra's Phoenix which are well positioned against the traditional composition of their deck. The problems arise when they have a Turn 3 Spectre and you don't have a Lightning Strike; or multiple Desecration Demons. Pack Rat isn't very scary; 3 mana to make a Rat that trades 1-for-1 with your 1 or 2 mana removal is to your advantage and otherwise they're a deck that tries to trade cards except you've got a lower curve and run more spells, so you have a natural card advantage that they can only make up through Underworld Connections (-2 cards though) which costs them life. The Rakdos Suicide deck is well positioned against this deck because all of your creatures are good against removal and you have a lot more answers to their problematic cards (Nightveil Specter and Desecration Demon) than even the RW Pyromancer shell.
Mono U Devotion. This is the deck that forced Red based aggro out of the format; almost entirely on the strength on maindecking 16 hate cards (Frostburn Weird, Nightveil Specter, Master of Waves and Tidebinder Mage). These cards would wall your beaters, generating effective card advantage for them, then power out devotion for huge Master of Waves that would then kill you. You'll notice that there are no 1 drops in my list (in the maindeck anyway); this substantially weaks cards like Frostburn Weird and Tidebinder Mage; who's main value in the matchup is shutting down your 1 drops. You've also got more removal and interaction than a normal red deck, which positions your better against their key cards. Basically, you're already pre-sideboarded for this match, and while I don't think it would be favourable, it should be reasonable, which is a huge step forward.
UW Control. At some point, this matchup became problematic, mostly due to the inclusion of 4x Last Breath. That gave their deck enough early interaction to survive and power out a Jace or large Revelation. Your cards were all good, but you just weren;t quite interactive enough. RB interacts with this strategy much better than RW; Thoughtseize and Dreadbore are extremely powerful against their strategy, and the sacrifice effects help protect your key cards from effects like Azorius Charm, Last Breath and Detention Sphere. Post board Rb usually has a substantial advantage because your proactive cards answer their reactive ones at a substantial mana advantage.
Post BNG, these matchups don't change too much. Mono U and UW don't change at all. Mono B gets Bile Blight and Drown in Sorrow (boo and booooo!). That's unfortunate, but look at the creature base. Firstly, we're not running a LOT of creatures (like a BTE deck would) so you're not going to be extending into them too badly. Secondly, all of the creatures are resilient to removal. Necromancer affects all of your humans (Pain Seer and Young Pyromancer) greatly reducing the power of these cards; Phoenix can be rebought. Thoughtseize can proactively protect your board. The sacrifice effects can fizzle a Bile Blight."
