I've taken three approaches when overwintering:
1) Bring the plants indoors with no pruning at all and treat like a houseplant - don't let them go dormant.
2) Bring the plants indoors after pruning just the smallest branches off.
3) Bring the plants indoors after pruning down to a stump (both branches and most roots), ensuring at least 6 growth nodes remained.
With both methods 2 and 3, the desire was to make the plants go dormant over the winter. Dormant plants don't require much care. Feed and water less often, and provide less light. In the springtime they came out of dormancy and I gave them more light, water and food. They did create more branches. Since chiles only put out pods at the growth nodes, as lek said, more branches typically means higher yield. The big thing here is that the plants require less work when dormant. Depending upon how many plants you grow and the amount of effort you put into the plants over the growing season, having a period of dormancy gives you a nice break.
I didn't care for the plant shape after method 3, so I won't be doing that again, though it did also save the most space. I would definitely do method 2 again. Method 1 is fine, but "oops" can happen more readily than in method 2, as if you have them in a room you don't frequent and forget to water. Oops, they're dead.
I kept one plant going 4 or 5 years, using method 2. It was fine through the third year, but then production backed down so it wasn't worth keeping it going to me. The continued production year-over-year depends upon the variety. Pubescens tend to be more prolific bearers beyond the first couple of years. But then, a lot of it has to do with the grow environment over the winter, too. Another consideration is pests. Every year I overwintered, aphids came out in abundance in the spring. I bought ladybugs to get them, sometimes more successfully than others. That's more something you just have to be on the lookout for and be ready to deal with when it happens.