after reading all that, while I still prefer to push them more toward a skirmisher + fortified defender (collateral + withdrawal + increased Def strike + Defender-like promotion,
Lacking that (as thought OP by some) I think I could go toward :
4str, +25% inside cultural borders (attack&def), + 25% CD, -25%CA, collateral, defensive strike
making them 5str attack inside borders, 4str outside 6str defense in cities.
thus, archers are as strong as bronze axes inside your own culture, and even better as they do collateral in attack, are as strong as iron axes in city defense and do defensive strikes.
and mainly, inside borders, archers are 1str stronger than bronze warriors, both in counter-attack and in city-defense.
NB: with this setting, archers str scales less favorably than bronze axe with additional %modifier : combat promo, other promo, terrain defense as they have a small base str, so bronze axes still get a slight advantage which IMO can compensate the other perks of "new" archers even in your home territory;
-->a lvl1 bronze axe is better than a lvl1 archer (5+20%= 6 instead of 4+45% = 5.8), even in home territory....
however for defending cities :
not counting the 25%fortification : a lvl6 axe is needed (combat5) : str 10 versus combat5 archer : str 10 ...
with innate 25%fortification defense, an combatIV axe is better than a combat IV archer (10.25 vs 10.2)..
then with culture defense... (20%) combat III bronze axe becomes a better defender than combat III archer (10.25 vs 10.2)
..etc not counting defensive strike or possible collateral/withdrawal ...etc
however outside your borders, archers are "just" better than axes or bronze warrior in open terrain, and worse than both against cities (25%-45% difference) and plainly worse than bronze or iron axe.
listening to Qgqqqq I would think that exchanging the collateral for an innate +15%withdrawal / opening the flanking I promotion would still be nice and would not cut into the catapult niche (collateral) nor the horse niche (withdrawal... but no move left after the attack) : 50% withdraw with flanking I and defensive promotion.
I'm not sure such a "new" archer would still be prefered versus axes or horses but at least a "builder civ" could get a very long way using only them in order to defend the empire against anything save huge arcane/priest-led SoD
and if with we take firearrows to +1str, +50% vs cities,
an archers with firearrows become better than bronze axes anywhere.... *(save for scaling with promotions, see above)
(5+25% +withdraw or collateral against cities), but less good than iron axes or enchanted blade bronze axes.
thus the equilibrium is met.
in the same way, iron-longbows (6+2) with firearrows (+1) would be better than iron champs (6+2) everywhere ... but not mithril champs or enchanted blade iron champ.
(if longbow lose the metal promotion they would need a base 7str IMO / same as ranger... or at least 6str (same as HA) + something... ... collateral ?
+withdrawal? something else ? +20%str ? never-ending defensive strike (giving blitz should give this effect) ? ... those are F..ing longbows FFS! you don't charge against a wall of longbows.. you'll die if you try... that's worse than attacking a legion's shield wall !
then there is a need to balance with horses : but movement and vs archers or vs FS is already good.
and with recon ...
actual recon are also balanced : less str in home territory or city defense, equal str out of territory, better str against cities.. (-20% instead of -25%) + they get the %animal.. and the +1 move
... my further 0.2.