I personally would like to have both transmission and oil temperature gauges without having to use a scan tool to monitor stuff like the trans temp. However, if I were told I could only do one my first priority would then shift to trans temp because it frequently can get into ranges that cause severe breakdown of the fluid. You want that temp down in the 170* range. Anything over 200* and youre subjecting your fluid to a temperature that will start to break down the fluid and is kinda rough on the trans.
Now if you run synthetic trans fluid you have a little more cushion but even so its just good all around practice to keep the trans fluid around 170* or so.
People change the oil frequently enough that temperature stresses there are not as significant typically though they can be. But you dont want the oil temp up too high because it will start to evaporate off the smaller hydrocarbon chains in the oil and cause evaporation boil off. Likewise, you dont want the oil too cool either because then it cannot evaporate out any fuel or moisture contamination which when in excessive amounts can thin the oil out to dangerous levels or cause sludge and varnish build up.
