Bryant and Carrier are the same equipment manufactured by the same company. Carrier will have a few additional models that don't exist in the Bryant line up. In some cases Bryant models may be cheaper than the equivalent Carrier model.

Carrier/Bryant, Trane/American Standard, and Rheem/Rudd are considered the better brands. However all manufacturers have equipment problems from time to time. In addition most equipment failures are usually the result of a poor installation. A bad installation can ruin the best equipment.

The Carrier Performance series is considered a middle of the road model. It is a good choice for a cold climate. Be aware there are several Performance models so you have to be more specific of which you are considering.

All furnaces have heat exchangers. A 2 or 3 stage gas valve means the furnace can operate in low or high stages, or low, medium, or high stages. A 97% efficiency does not necessarily mean more features. You can find high efficiency furnaces that have few features.

There is always a potential for more features causing more repairs. If you find a good HVAC contractor and choose one of the better brands you should be fine.