I am answering on a hunch here, but getting growth hormone out is very dificult if your growth plates are closed even with perfect training and diet, once you reach maturity. Only huge doses and a long exposure to the growth hormone (1year+) will make you grow bigger, shorter exposure usually burns a shit load of fat and has anti aging properties, so you can be more leniant on your diet, I remember watching an interview with Cutler talking about his diet consists of Pizza and other junk food, and he can do this thanks to HGH. Most of changes on the HGH are permenant, ex: if you become bigger on it, it will stay pretty much forever since it can also thicken your bones (once again think about the world's top bodybuilders with their portruding jaws, chins and foreheads, these are all side effects to high usage of HGH)
Testosterone levels make you go into an anabolic mode and they make you grow, temporarily, once you come off due to low/non existant levels of test you become catabolic and that is why the majority lose some/most gains they have gotten (PCT dependant)
To answer your question, both at the same time would be ideal to grow since together they are incredibly synergetic. But for more immediate strength gains and size gains, testosterone is more desired.