IME, high power access points (with or without a router is irrelevant) are primarily of use when using two or more access points to construct a wireless link - usually one that you are not having any laptops connect to. Fiber is always preferable to one of those, but sometimes you don't get a choice.
You may get some benefit from using better antennas, since (as mentioned by jerm) they help with reception as well as transmission. Using better antennas and turning power DOWN is often helpful, or at least as useful and not as annoying to anyone else near you (for whom your high-power signal is just high-level noise.)
If your desired result is better wireless coverage, rather than crank up a high power access point, you will usually be far better off to run wiring and place additional access points (quite possibly with the power turned down, unless you are in the middle of nowhere.) Don't link access points by wireless - that instantly cuts your wireless performance potential by half or more - use wire (if between buildings, use fiber) to put them on the network, and only use the wireless to link to your mobile wireless devices (such as your laptop.) Give any device that sits still and has a wired port a wire.