AoE2 is technically the best game of the series. But AoE 1 will always be my favorite due to its setting. Ancient times is more appealing than middle ages for me.
But yeah, AoE1 has lots of issues ranging from technical limitations (mostly the fucked up AI pathfinding that even unofficial patches and the Definitive Edition re-release hasn't fixed).
Unit balance is ridiculous, RM is mostly archer dominated (by archer I mean chariot archer in early Bronze age) and DM is mostly centurion+siege warfare with some exceptions (e.g. Legions or Elephants if your civilization has a unit bonus for them). If you do survive early rushes and everyone runs out of gold, the civ with chariot bonus wins.
Cavalry becomes useless beginning at late bronze age and Cataphract was a ridiculous expensive unit upgrade that barely changed its stats from Heavy Cavalry, even after the unit was rebalanced in Upatch/DE it still is a debatable unit.
Civilizations were also balanced around these two game modes and Hittites were ridiculously overpowered before uPatch/DE, they had almost every unit of the game available.
My opinions about AoE3 are very limited, I haven't played multiplayer but even singleplayer is not very appealing for me. They pretty much wasted one of the most interesting eras of human history (colonization, napoleonic wars, american independence, american civil war) choosing to ignore all these events but instead make a campaign about a fictitious secret society. Even the expansion campaigns haven't changed much about it. Technically, the inclusion of Home City feature is very interesting. It's like in AoE2 each civ have different bonuses that you can choose before you play, so you had to be careful about which features you had to sacrifice considering your enemies/map type.