The Light Dragoons aren't awful, but they're in an awkward place, it'd be nice to have an actual unit of light, melee centred cavalry for the British.
It's not like they didn't have them, 4 Hussar Regiments and the KGL Hussar Regiments as well.
The Hussars (generally) were all Light Dragoon regiments (at least, in the KGL they were) and were renamed and adopted new uniforms. That's all.
Yes, they were essentailly 'fashionable' Light Dragoon Regiments, but the British initially formed light dragoon regiments to be their answer to the Hussars used on continental Europe. There's not that big a difference, technically, hussars should even have guns, but that would make them OP.