When faced with a choice between stress related burnout or breakdown, burnout is generally a better choice.
Burnout is similar to physical exhaustion. When we do the same physical work over and over again, at one point we become exhausted and the body gives up on being able to do that work for a while. Burnout is more of a long term mental effect: when we perform the same activity due to stress, at one point a realization might strike that there is no longer any meaning to performing that activity and we completely lose motivation.
At best, burnout is a semi-conscious block for preventing damage caused by stress. Unfortunately, burnout can also take out the meaning from many related activities and might lead to depression.
Burnout might be a blessing in disguise if you decide to look at it that way. The key to dealing with burnout is to stop looking back at the past and start looking forward into the future. Out with old shallow values - in with new meaningful values.