I tested battles of various sizes with my friend who was playing Iberian javelineers versus my Ptolemy slingers, and the results are always the same: the slingers defeat the javs. In test runs of 25 slingers vs 25 javs, 50 v 50, 75 v 75, and 100 v 100, where we tried one of these three settings: 1) we set the armies next to each other both on "passive" then clicked "aggressive" at the same time (we practiced this many times to get the timing down), 2) we started the armies on aggressive and each clicked on the opposing army's front soldier, or 3) we started the armies on aggressive and had one of the two armies attack the other by clicking on their front soldier, the slingers always win.
Why does this happen? Javs and slingers have the same intervals and the same resistances. The slingers have 45 range v the javs' 30 range, which is why we tried setting 1 (refer to above), but even with the javs 16 pierce damage v the slingers 11.5 pierce and 1.1 crush damage, the slingers still defeated the javs every time. We tested setting number one with them at least two times with each of the numbers above of 25 each, then 50, 75, and 100. If anyone is interested in seeing this for themselves, I'd be happy to test with you. If you see some big/significant flaw in my testing, let me know.
Best,
EP