Hi Atomant - it is reassuring to find someone else experiencing similar issues. I just bought a PODHD500X, and I was initially quite pleased with what I perceived as a vast increase in the clean headroom on my Bassbreaker 007. On comparing results on other amps, including my Blackstar HT5R, I now realise that there is a significant signal loss through the POD. Like you, I got significantly more volume, gain, and frequency response, with the guitar straight into any of the amps. With no effects or amps on the POD chain, I have to increase the Mixer volumes by 6-8db to achieve the same volume and gain and, even then, there is noticeable tone suck. You can obviously get acceptable volume, gain, and tone, by inserting boost, EQ, and amps into the POD signal chain, but I think the natural characteristics of different guitars will inevitably get lost.
I also have a GT100 and ME-80 and I agree that they appear much more transparent. In fact they have a tendency to boost rather than loss, even when you don't intend it. You will know that the clean channel on the Blackstar HT5 is very clean, and the Dirt channel is very dirty (unless you are a metal head!). The GT100 will normally make the Dirt channel unusable for anyone that just wants a modicum of dirt. I found that the solution was to reduce the GT100 guitar input level by 10db in Global settings, and then adjust the volume on the Clean channel and Gain/Volume on the Dirt channel to taste. Messing around with these 3 parameters can achieve pretty much anything when using the GT100 on the HT5. Unfortunately it doesn't work so well on the Bassbreaker as there is only 1 channel - to get clean headroom you have to turn the levels on the GT100 and the Gain on the amp right down, which results in very little volume even with the volume on the amp right up.
As various contributors to your thread have commented, nothing is perfect and it's all a matter of getting the best compromises possible for the result you want with the gear you have.