I don't think of it as one or the other. I train for TRB, and I would plan to TRB in a real life situation. It is the better choice, more or less indisputably. However, to me, second strike isn't about choosing not to TRB. It's about in the stress of a real life situation, things don't always go as planned. You may forget your training and just squeeze the trigger as fast as you can. You may be injured and have trouble racking the slide. You may have to hand the gun to someone else who has no idea how to run it.
In all of these situations, a gun with second strike capability is superior. It is not a significant differentiator, and I wouldn't make a buy/not buy (or carry/not carry) decision based on it, but it is worth something.
My carry gun of choice is an HK with their LEM system. It is similar to the Berettas action, except it does have a second strike. It is a very heavy second strike (like 15-18lbs), as the gun is not designed to be fired without being cocked. But its there, and I prefer that, even though I will likely never use it.