I think it needs solid state, whereas the Terror has a valve pre-amp.
IMHO this is where to start:
What makes you think it's the amp and not the cabs or settings?
Each model of amp tends to have it's own personality. So it would be helpful to understand what you are experiencing and specifically what you want. Also it means that it's best if you actually try before you buy.
A common concern with the original Terror Bass amps is the preamp has quite a bit of gain. Some users were frustrated because they could not turn the Gain control above 9:00 or so without getting distortion. If you can't get a clean sound, set the input to passive and turn the Gain down. As long as you can get the desired tone, it doesn't matter how low you have to set the control.
The Mk2 Terror Bass amps have less gain and a clean switch, most likely to address this concern.
The Terror Bass uses a Fender tone stack. This means it's not capable of producing a mid boost. Flat should be with the Bass control open a hair, the Mid control around 3:00, and the Treble control off. I suggest starting with the tone controls set accordingly.
If your Sterling has active EQ, I suggest starting with the Volume wide open and the tone controls in their neutral position...no cut or boost. First, adjust the amp's controls to get the best possible sound. If you can't get all the way there, then make subtle adjustments using the bass's tone controls. The key work is
subtle. In other words use just a little bit of boost or cut.
Most of the Bad Company hits I remember had pretty vintagey sounding bass. The videos of the Sterling I have listened to suggest it is a fairly modern sounding instrument?
The Terror Bass can be fairly bright and my guess is the Sterling can also be fairly bright. You may need to roll some of the highs off with the bass.