Testesosterone replacement is meant to elevate your testosterone output artificially.
Biotest stacks are meant to elevate it more naturally.
I am not sure how much Biotest stacks elevate Testosterone levels and I'm pretty sure that every individual will respond differently. There was a study done by them a few years ago that examined the effects of the original TRIBEX-500 on cyclists if you want to get an idea. I don't know where it is so maybe someone that feels like searching the site can find it.
Now theoretically if a Biotest stack worked as well as hormone replacement you would have the same side effects you are speaking of. Once testosterone is in your system it's test (either free test or bound to SHBG). It can aromatize to estrogen, it can be converted to DHT (one of the main factors in hair loss).
The only difference I would imagine (Cy Wilson can answer this better than I) is that Biotest stacks will cause less, if any shutdown of your HPTA axis...so that if you were to stop taking them your natural testosterone levels would not plummet whereas they WILL once you stop the HRT.
By taking HRT you are putting exogenous hormone in your body. Since your body is getting it's test from another source it no longer sees a need to produce it on it's own, in fact your body think it's advantageous to stop producing it to help maintain homeostasis and thus not be in a supra-physiological state.
I hope that helps.