I have experimented with several setups in the past couple of years. I currently use a skinny 120 lb racing tire on a 700 C bike for longer, steeper rides and an insert on a 26" bike which is on either a 559 or 590 rim for flat, in town 5Ks. Both do quite well. Any given 26" rim will NOT fit any 26" bike. Finding a rim and tire to match a given bike can feel like hitting the trifecta. My 26" airless insert will add the least unnecessary distance to a course. When using 2 riders, I use whatever set up will best match my partner's for the sake of agreement.
What does not work well? I got a mountain bike with 65 lb tires after seeing Pete Riegel's meter mounted on one somewhere. The first time I measured a 5K on rapidly rising temperatures, I had to go back and redo a mile. That lead me to a 75 - 95 lb tire for that bike. I had to redo a mile for agreement on an out and back 10 miler pumped to about 85 lb. At 95 lb, I had no problems with agreement. But I was making courses longer than buddies with 120 lb tires.
My first airless tire was the insert commonly available at Wal-Mart and it works well. Only problem is that it unpredictable regarding recalibration being shorter than calibration: the counts are almost exactly the same but .5 counts longer on one of the 4 recal rides and you theoretically have to go add distance to the course.
65 lb class airless tires (not necessarily inserts) are VERY hard to pedal. You sometimes have to (had to) pedal down hill. Furthermore, the best whole airless tire I could find for the old mountain bike would sometimes show a radical difference at recalibration like the tire settled or repositioned itself. Duane Russell has airless tires on a 700 C bike that work fine. I figured that was worth a try so I got a 700 C bike this spring. Then found out my bike shop could not find rims for the ones Duane uses. Also, airless tire sources have been tough to communicate with when I have a problem. The Wal-Mart mountain bike class airless insert I had on a rear tire was also a contributor to pedaling difficulties.
Mountain bike treads and be such that they will pick up small sticks or rocks after calibration and artificially lengthen a course. Finer treads and treads "over toward" bald are better about this.
All of this is based on my admittedly limited experience.