These questions were asked by a fellow Orange County Triathlon Club Member. I've attempted to offer a brief comparison of two specific shoes.
Q. Also, what's the difference between road bike shoes vs. tri specific shoes?
A. In the comparison of two LG shoes below I've highlighted a few differences between a tri and road shoe. These differences will vary from shoe to shoe but I hope it gives some insight into differences.
Pull Tab - A large pull tab on a tri shoe helps with quickly putting it on. This is especially helpful for those who keep the shoe clipped in to the bike. This helps with a quicker transition.
Strap Direction - Most tri shoes have straps that open away from the bike so they don't get caught in the chain when clipped into the bike.
Ventilation - Most tri shoes will have very good ventilation so wet feet can quickly dry out. This isn't to say that road bike shoes have poor ventilation.
Strap count - Most tri shoes will only have 1 strap. Again this is to make it easier and quicker to strap on during a transition especially for those with bike shoes already clipped in.
Q. How much speed is gained when using a road bike shoe vs. a mountain bike shoe?
A. I assume this will vary from person to person, but a more solid platform combined with proper technique should improve speed with a bike/tri shoe. Maybe somebody else out there can offer some links or insight. Apologies for not being more helpful.