In all cases the GTX is a "bigger" compressor as far as I can tell, so laggier but flows more. In the case of the 3076R comparison I have the impression the HTA > GTX as the HTA pushes to the limit of the GT30 hotside anyway, as far as I am concerned. In the case of a GTX3576R vs HTA3576R the GTX may have a flow advantage but with the GT30 hotside I consider the GTX3076R a turbo that is quite a bit laggier than the HTA, but with no additional flow.
In regards to the GTX vs HTA 3582 things change a bit, the HTA3582 *ALSO* will be quite a bit more responsive than the GTX - but the GT35 hotside has a bit of room to move over the flow the HTA3582 can provide (hence the HTA3586). I have the impression from results I've seen that the GTX3582R is probably closer in flow to the HTA3586 than the HTA3582, and response somewhere in between the two - which makes the GTX a bit of a different beast.
As such, I think the HTA3076R > GTX3076R overall as a product for that power/response area.
The GTX3582R is more of an alternative to an HTA3586, and I have the feeling that the GTX may actually provide a marginally better compromise between power and spool than the HTA3586 - however if you don't need quite that kind of power then the HTA3582 is definitely much more responsive and a capable upgrade over the normal cast GT3582R.