I have to bike in my road shoes, because I have SpeedPlays and I can't pedal with running shoes.

You get more power on the bike with clipless pedals.

So, I wear my bike shoes out of T1 and my running shoes out of T2.

It's all about what you are comfortable with though. I see many people who use their running shoes on the bike and run.

Best of luck! Let us know how it goes.