dogs
11If both boom up, Byz pure ECats have no chance vs Goth halbs + few treb.
Its already been mentioned but if its 1v1 and both civs boom up, other civ should win. For example, in a pure boom situation, getting around 30 FU catas will take at least 35 min (maybe longer). If against goth, goth can have a 30 halb army and some rams by 30 min, 31 min latest, and by about 32 min should have a castle with the 50% faster barracks tech done. Arena and bf are the only maps where you can really make catas, but they arent cost effective (usually).
And to answer the question, palas, arbalests + halbs, mangudai, are good counters.