2. So both fast AND stealthy?
Regarding the Felines:
*It takes a National Wonder (previously a world wonder and I'm not so sure that it was right to change it) to get them.
*On the core game their strength comes out the same as an ambusher. They are harder to get and come up later.
*On Size Matters they come up a little less in strength BUT they CAN merge - still don't think that's enough given how much later they're introduced. At their introduction, most core combat units are around str 4.
*They have the same strength, either way as comparable dogs.
*They can be seen by dogs
*They are far slower than ambushers who have 2 mv.
*Their promotion options are quite strong for attacking but reduce their withdrawal abilities and ability to capture units (they tend to kill and eat and not care if the enemy surrenders.)
So to give them +1 mv, able to ignore terrain, and a size matters category upgrade somewhere (I'm thinking Group Volume) and we'll make them a touch better than ambushers. Better when attacking. Usually a bit worse when defending. Unlike Ambushers, they're strongest developments will REDUCE their withdrawal and abilities to capture but they can more quickly become better attackers which is what I would usually WANT for my ambushers anyhow. Speed-wise they strike me as a unit that should be patrolling the wilderness for their master's benefit and RL great cats are able to get around in the worst terrains. Also consider that the best units to counter them with, Hunters, are also the types of units that are best targeted by the Ambusher so these cat units are an evolution past that into the realm of units that can strike at larger and more powerful groups with impunity if the dog's detection abilities aren't accompanying those groups. Thus, very good at striking merchants, small military forces, escorted workers and other units that can be found to take advantage of. Also makes them a great surprise defensive force when at war that can quickly respond to enemy raiders surging towards your borders away from the main fighting.
Unfortunately though, at the moment, they're next to worthless because they aren't strong enough nor fast enough to find any real solid use except against the weakest of unsuspecting defenders.
Dogs need the added movement to more fully embrace their role as a wrapup attacker against units that are otherwise strong at fleeing. And I also don't think dogs would be much hindered by terrain. Both animals, being quadripedal, are really excellent at maneuvering in wilderness environs, far moreso in more difficult terrain than we are. The major exception could be we could be better at some more extreme acts of climbing.
In short, these are just feelings I have as a player going through the game - that these adjustments would be of major benefit to the feel and balance in the roles all said units play.