If, as you say, Bristows financed their aircraft, then at least they can sell the equity in the asset. That is something I believe CHC could not do, hence rushing for the shelter of Chapter 11 protection.
Many of those aircraft will have been financed pre-2014 at a premium. Demand is now oversupplied and capital values have dropped. You're correct that they could release some equity, but that's addressing a symptom, not the disease.
The cash burn is far too high, and unless they can reduce operating costs, releasing equity will just give them a short lived period of breathing room before they burn through the equity and run out of options.