1: They can't skirmish. That is, they can't fire and run. Every ranged unit in the game can fire-move-fire. Not the Longbow. He has to turn and face the enemy, sit down for a quick picnic, talk about the weather, butter his scone, eat it by chewing 40 times per bite, stand up, slowly and leisurely pull back the bow and fire. Repeat. So the Longbowman gets to use the advantage of his range maybe ONCE before the enemy has ample time to move in.
2: The auto-attack is ineffective. The Longbow's advantage is supposedly range, but an enemy unit has to practically pick the longbowman's nose before he'll respond and fire. So the only way to get the Longbowman's advantage to work is to micromanage him and fire on the enemy in the first ten milliseconds he appears on the radar.
3: As if they weren't bad enough, if you want to upgrade them and give them shiny pants you have to invest in a homecity card. Everybody else gets their UU guard upgrades for free, but the Longbowman has to br given special attention. I'm surprised the balancing team didn't add an even simpler technology: Arrows - Allows the Longbowman to fire arrows...when he's darn good and ready. In the meantime he can do some pretty mean "Slapping" melee damage.
Longbows are a good counter to things like Janissaries and Skirmishers when, you know, you build a 100 of them. These deficiencies are ludicrous and keep the British down. I hope they're tweaked soon.