I was wondering, how long can you expect to stay alive with an uncontrolled engine fire ? I can not find written somewhere which way is the best.
You're not going to find anything written about how long you've got...because any number of possible circumstances might have occurred which caused the fire. How long depends on the cause and the reason you can't contain it. How long the fire burns is really quite irrelevant, because you're going to take what action you can. If you don't make it, you don't make it, and if you do make it, then the time is irrelevant.
A friend of mine died a year ago in an uncontained fire when it broke out 300' in the air on takeoff. He burned all the way to the ground, a short distance away, in a P2V.
Several years ago as I approached an uncontrolled field at pattern altitude, I began to smell smoke. I executed an overhead break pattern as I passed over the runway and made immediately for the numbers. By the time I passed over the numbers landing, it was hard to see in the cockpit, and by the time I reached the first runway exit, it was difficult to see because of the smoke obscuring visibility and burning my eyes. My lungs felt like they were on fire, and I had little doubt I was on fire. It happened fairly quickly, and while fortunately I was literally approaching and over an airport, any earlier or any delay in addressing the problem, could have been costly.
Most of the time, and engine fire is not a big deal. Other times it's a very big deal. An emergency may very well be such that it's not survivable or recoverable. Your fate is sealed from the start. The loss of the Valuejet DC-9 in the swamp is a good example. They didn't sand a chance.
As for the second part of your question, you're asking which procedure is best...getting on the ground as soon as possible, or taking your time to fly a full pattern while burning to death. Is this really such a difficult choice?