It is often a question of what you like, what you don't like, and how strongly you dislike it. Two strokes can be quite usable provided you don't mind mixing the fuel, being surrounded by noise emissions rather like an old cab that is way past its use-by date, and getting yourself smoked on the hoof while you are trundling the thing across the grass areas. On the more positive side you can use them on outrageous slopes, though it is dangerous to do so.
I personally find 4 strokes easier to work on, and vastly more prone to staying fixed once you fix them. However if you rather like the idea of keeping a small tool-kit close to hand whenever you run your mower, a two stroke may be just the thing.
So far as durability is concerned, I think a good example of either type can last a very long time if you look after it. You may have to pay quite a bit of attention to the spark plug of a two stroke, but you certainly have to pay attention to keeping the sump full of clean oil with a four stroke. Emissions laws permitting, they both have their place. Personally I'm rather more comfortable with a two stroke engine on line trimmers, because I'm wary of mist-lubricated four strokes. That is just prejudice, though: a long time ago I was wary of fuel injected car engines, because the early examples were so bad.
