Total Distance or Total Time as a Gauge for Overall Effort?

Same here. Between time & distance, I use time, but not only time. The stress level matters.

^^Yep^^. I'm a distance guy too.

I measure overall effort by training stress (time and intensity).  I agree that distance becomes a factor since that's how races are measured, but you should have a good idea about what type of time and intensity it should take you to cover a given race distance.

For example, in training for a 36 mile bike race I did a couple of weeks ago, I was doing long rides in the 5+ hour range, some over 100 miles.  Why...because I knew the 36 mile race was going to take me 3.5 hours due to it's difficutly.  I knew I had to simulate the time and intensity of the race in my training...I couldn't just simulate the distance because there isn't terrain that difficult where I was training.

When I was just running I always went by miles.  Now I go by time except in the pool. Why? Because that is what my coach puts in my plan.  The time pretty much corresponds to a training pace/distance but it is always by time.  For my IM the rides are 5.5 hrs, runs 3.5 hrs, etc.

enjoy,

Duane

I use whatever is most reproducible and convenient.

Yes, TSS scores and all those fancy power measures are awesome, but if you don't have a powermeter, or a swim/running, forget it.

Distance is good on similar courses, but fails for hugely variably course elevation/conditions. Time is good to a point, but you can end up with a lot of variability depending on your effort and level of fatigue.

I base mine on my most commonly use routes and available equipment. Which means that most of the time for me it's distance since most routes are similar, but on hillfest days (mountain terrain climbs) I'll usually switch to time. 

Between flat century rides by me (~1,700 ft) and ones up in Wisconsin that can have 8,000-8,500 ft with more technical descents I can't let it out on. There can be 45-60 minutes difference in a "century" ride. All centuries are long, but that's still a significant difference in the amount of time.

To deal with that, I'll consider the distance, the terrain and the conditions of the day to get some idea of how long it would take, and then adjust the route accordingly (as best possible) to come in closer to the time I want. Sometimes I do have to just get through the distance if that option isn't available, but if it is, I do. And that means I might go a little farther if I'm going noticeably faster than I thought too.

Races might be in distance, but there is no way the Arizona and former St George courses would be considered "similar". You know darn well you're going to be out there longer for St George and should be training for that.