this poses no problem to empire building, if noone has iron weaponry then evrione is on the same level, in terms of armament, and must atempt to win by using superior skill, strategy, organisation, quantity or quality
tehnology would definitly be diferent and this would afect economy and architecture, but probbably not as much as we would think
etruscans were big iron producers, so probbably the same would go for bronze, and romans would inherit this, but thre were strong bronze age cultures in the balkans and these would probbably maintain their power longer, limiting roman conquest
a lerge empire that thinks like rome did, would probbably go for the cheapest forms of weapons that are still efective enough, so they would limit the amount of bronce per legionare, using it to strenghten leather armor or make spikes on top of wooden speares, mass produced axes instead of swords
even in OTL romans were often "outgunned" by longer swords, skilled warriors, better metalurgy, deadly polearms, mounted archers, etc... they had a way of winning in the end, becouse they were sistematic, well organised and stubborn, or just becouse of superior tactical formations
all this had little to do with iron