Did a few more tests 1vs1: Some equites vs. vanilla slingers, vanilla archers, and forester warbands, and dacian archer warbands. Their are a few patterns emerging:
1. High melee archers like the foresters seem undecided. They will pause and stand well within their range, rarely firing, mostly just standing to receive the charge. They will win in melee thanks to their spears and high attack, but a wide horse formation on the charge can inflict very high casualties on them. Still it's a waste not to make the most of the high missile attack and range. When I play as the foresters side, the cav don't even reach my lines most of the time, and when they do they are easily beaten.
2. Most mid or low melee/moderate missile attack archers will stop at about the limit of their range, then restart walking. Sometimes they stop and fire a few rounds. Once, one stopped at the very end of its range and let loose quite a few vollies causing me heavy losses before melee. (Never could get it to do that again--I think it happened because I used 3x and didn't go back to 1x before they hit the outside of the range.) Sometimes they don't fire at all and wait for the charge.
3. Low missile attack/low melee slingers advance, but never try to shoot, they stop at about their range, then turn to run. Occasionally, they kill 1 or 2 mounted men in melee. Other than that, they are dogfood.

AND THE MOST STUNNING/AMUSING OF THE TESTS...an accident...I took the field with 1 Roman archer vs 1 Roman archer by mistake:
My counterpart walked up through a barrage of fire. He didn't run, he didn't stop at range. He just walked up to within about 40 yards being massacred. After losing about 40% of his force, he decided to go to loose spacing, then walk back to a range of about 70 yards, and trade vollies. By the time he reached that point he had less than half his force left. After a few more vollies it ended with all but 6 of his guys dead. I "suffered" 4 casualties out of 81.