No. All current bikes are stiff enough not to shimmy on fast descents, and apart from that it has been proven that no energy is lost to frame flex.
They might feel a bit different, but I wouldn't overestimate the differences.
Marin is basically right about this, but since the OP seems to be new to these sorts of questions, I should clarify two things:
- Shimmy still exists; stiffer bikes tend to be less prone to it, but riders of new bikes still sometimes experience shimmy.
- Energy is absolutely lost to frame flex. Perfect springs don't exist; they all dissipate some energy. That said, the amount of energy lost to frame flex is so small that no one (to the best of my knowledge) has been able to measure it. The difference between frames is likely to be lost in the noise of any power meter, including SRM's "lab" meter.
I wrote a sidebar for the Fairwheel Bikes crank stiffness article that attempted to establish an upper bound for energy losses due to crank bending. (In other words, if all the energy that went into bending a crank was lost, how much would those losses be?) The numbers were small for a very flexible crank (roughly analogous to a Campy Super Record crank). The maximum possible losses for a stiff, modern crank would be even lower.
This is one reason why it drives me a little nuts to hear people talk about "power transfer." First of all, the term is meaningless from an engineering perspective. Second of all, all frames "transfer power" so similarly that no one has measured the difference between two frames. I understand and accept, however, that "power transfer" is just shorthand for "it feels stiff and fast."