That would work but bare in mind that the losses in the coax cable are quite high and sometimes what you gain with the antenna can be lost in the cable.
The AR150 is considerably slower than the AR300M in terms of processor speed so it all depends on your usage.
If you are getting a good signal outside you should not need the external antenna so could use your AR300M (no microwave losses!). You could do an improved version of what I did and put the AR300M in a plastic food box, run an ethernet cable down into the house. Have the cable coming out of the bottom so water cannot get in, and if it does it can run out. You could possibly save a bit by also running a cable for power instead of the POE injector and splitter, I am not sure.
Then an AR300M-lite in the house perhaps although an AR150 would work.
Putting the lite in the box would be slightly more flexible as you would then have a LAN ethernet connection free in the house, but you would need to build a custom image with LEDE/OpenWrt Image Builder to switch the lite’s single ethernet to LAN and turn on the radio in STA mode. Very easy to do and teaches you a lot about LEDE/OpenWrt!
A nice do it yourself budget project 