While Im a proponent of synthetics, gear oil is one situation where, from a performance standpoint, there is no benefit for paying the extra coin.
Now oil, yeah...just because synthetic is cheaper per mile in the long run.
I'm sorry, but I have to disagree ...
First let me say that my opinion is formed after personal experimentation over a number of years and vehicles, this is no "regurgitation" of what I've read on the internet, or heard from a friend of a friend.
I run full synthetic lubricants in my transmission, transfer-case & differentials on every vehicle I own, and conventional motor oil in the engines.
I can feel the difference in the way the transmissions shift, I've seen the benefits of the full synthetic in that application - now - on an off road vehicle, it may not make that much of a difference that you're willing to pay the extra for the full synth, but on a sports car where a tenth of a second makes a difference, I can attest to the performance enhancements.
Additionally, as Max has pointed out, the drive-line lubricants are changed less frequently than engine lubricants allowing the cost to be spread over a longer period.
On the engine side - over time the oil becomes contaminated with combustion byproducts such as, soot (which is too fine to be removed by the filter), acid, moisture, fuel dilution - if the engine is operated long enough, the oil will become hot enough that some of the moisture will burn away, but the remaining contaminants are held in suspension until the oil is changed.
How long do you want to leave that toxic soup inside your engine, knowing that every day, the acids are eating away at your bearing surfaces?
Personally I'm changing it out, and I am not willing to pay the extra for the synthetics, and, please be reminded, this is after testing with full synthetics, and synthetic blends.
The last thing I want to leave with you - research the Castrol/Mobil One "law suit" - see where the Supreme Court allowed Castrol to redefine what a synthetic oil is, and then decide if you want to pay as much as you're paying for what is, in all probability, just a better refining job - are you actually using a synthetic oil or just a highly refined mineral oil?