I think Ryu might have a slight advantage against Birdie. Of course if the Ryu doesn't know the matchup or is playing pretty dumb, Birdie can get through fireballs easy, but the hardest matches I had with Birdie are against Ryus It's weird to see people think Ryu is bad. I think Ryu is very damn good and can deal with everything thrown at him in this game. I know it's an appeal to authority but Infiltration also said he thinks Ryu is the best, but that guy is basically one of the best shoto players in SF4 so that might skew things quite a bit.
Birdie's chain definitely is great against fireballs, if it lands, it wins because the fireball passes through him during the throw animation. But the chain has limited range and at full screen the chain won't hit. Birdie's jump grab isn't too great at going through fireballs to be honest, because you have to time it well, I have been hit on the ascent and on the descent from a late fireball using this move. Also the HK version will basically only hit if a Ryu basically has never seen it before and he can obviously hit you out of it easy with a shoryuken at that point. Birdie can try to use the charge headbutt (hold P and release) to go through fireballs, but again I think a smart Ryu knows that throwing fireballs too close is trouble and wouldn't do it. EX buffalo headbutt goes farther and has armor, but I don't think a Birdie should be throwing it out too much in neutral even though it has armor and acts as a decent reversal, because it can be parried and even on block you can eat damage for it. I think once Ryu gets in Denjin mode his zoning is really damn good. It has multihit fireballs, the delay can mess with jump timing, and the fact that people have made guard crush setups and denjin setups make it pretty scary once he pops it. Even though parry isn't like 3S and he won't punish everything if he gets a parry like that game, just building V-trigger fast is a huge benefit and people getting a few parries means that a Ryu will most likely see 2 denjin modes in a round.