Only the TP-Link actually says High Gain, the Trendnet says High power. Might be the same but I'm not sure.
Beside the point that high gain might be 4-5 dBi at best. I highly doubt they come near to 7-9 dBi antenna devices, like the Alfa 9 dBi or the available (not sure if this is what he currently has, though) 7 dBi BearExtender.
Very important to realize that higher dB will give you a better connection to a network that is further away, but will give you a weaker connection to networks close by. Trick is to get the sweet spot. (Why EXACTLY ‘‘tis is true I’ll leave to the techies, but I know this from experience. I think it may be bec of the fact that higher dbi gives a longer range, but much more focus. Somehow leads to fluctuation or maybe it picks up more noise. Not sure exactly, but practically speaking that seems to happen.)
We are all missing a lot of vital information if we really want to answer your question.
To help us, pls go to Speedtest.net and tell us what numbers you get. We also (and probably more importantly) need to get information on your connection speed. I believe there is no way to get a good answer without special software. I’ve never used this specifically, but it looks like a free option that should do the trick. Pls test and post the results you get.
(It looks reliable, but I’ve never used it, so do so at your own risk I guess. I doubt there’s much risk especially if you test it with any half decent virus protection software.)