For those two particular rigs, I think the Winnebago is probably slightly better constructed than the Coachmen, at least based on brand alone. With any used RV the quality of care the previous owner gave is a very important consideration, and often trumps any difference in initial build quality (more so the older it is). However, I'd be more concerned about the layout and what works for you than the differences between makes. For instance, despite the gushing ad copy the dealership put together, one appeared to have just enough counter space in the kitchen to put down a spoon or a pepper shaker, but not both at the same time, while the other has at least a square foot more.
The appliances and other parts of the systems come from the same few companies regardless of who makes the RV, so there's not a lot to differentiate in them. The differences between brands are mainly in such things as roof and wall design/construction, attention to detail (which is rarely a strong point for anyone), etc.
Unlike some others here, I don't think it's at all unrealistic to expect that the appliances will generally work fine for the whole trip, nor for that matter that the chassis will hold up without major problems. There very well may be minor problems and being handy and having a few tools and basic parts is a very good idea. There are a lot of parts to be finicky, but on the whole an RV is not quite the soap bubble that some seem to imply. That said, they aren't overbuilt at all, and one does need to be wise and take care and treat things with an appropriate degree of gentleness.