http://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing, the issue isn't that the peaks are high, what happens is when you crank up the power, the "perfect" sine waves get distorted because at high out put power level, inexpensive amplifiers can't produce a perfect sine wave, you get cut offs. If this was not OFDM, this wouldn't really be all that much of a problem. OFDM however crams a bunch of sub-carriers together in very closely spaced frequencies. So if transmiting at something like 20MHz width and 2.42GHz, what is actually happening is you might have 16 sub-carriers being transmited in that frequency spread, one at 2.423GHz, one at 2.424GHz, etc. The wave forms have to be reasonably precise, otherwise you cannot distinguish the closely packed wave forms. So wave form distortion will result in read errors on the receiving end.
Really good high power transmiters have much better amplifiers that are able to maintain wave form shape and coherency at very high power levels. This isn't something most consumer and even business access points and routers need to worry about. The cases were a few dB of signal difference would truely mean much higher speeds isn't going to be a lot, because you don't have gradual drop-offs in received power, you have big drops as you move between obstructions. So the change in signalling power from the AP is going to mean relatively little in terms of ability to receive that signal.
Outside it could mean more pronounced changes and receive signal strength and performance as drop off in signal strength is exponential, but fairly smooth, meaning a change of just a few feet can result in a big drop in speed, where as constant Tx power through better amplifiers would mean a much smoother change in performance outdoors. In doors this doesn't really matter.
This is also why outdoor dedicated bridges, for what they are, tend to be a bit on the expensive side, because the manufacturers are often dedicating much more expensive components in to them to be able to manage 400mw, 600mw or even a full watt of transmit power relatively cleanly (and often even there, at the highest signaling rates they have to back off power a few dB).
This also gets in to part of the reason why different APs and routers can have such radically different performance at different signal strengths (and the client also comes in to this too, with how good its amplifiers and signal processors are). Antennas of course come in to this as well.
Anyway, that is why one AP at 300Mbps is not likely to perform at the same level as another AP at 300Mbps. Even with identical antennas and transmit power, one could have better amplifiers leading to a much cleaner signal or any number of other things.
One of the biggest take aways is that, like most things, there is no free lunch. You want high power? Want high speed? Want low cost? Pick any one. Occasionally with a really great design you can pick two, but that is the exception.
