Does quality of garrison troops matter in happiness bonus??

In MTW and STW, it was possible to use peasants as garrison troops.. 100 peasants would give the same happiness bonus to a province as 100 Janissaries or 100 warrior monks.

Is it different in RTW? It seems that whenever I pull an Urban Cohort out of a city, the city tends to get very much more pissed than when I pull out some Hastati.

Also, do cities actually get angry about recruiting and/or troops leaving, as in the first two Civ games??

It doesn't seem like it. What matters is the size of the city. 4 peasant units could easily add 80% (the max) to public order in a small city but add only around 10-15% if you let it get too large.

Quality of troops does not affect the happiness. It didn't in MTW either.

So train peasants since they are the largest and cheapest unit to garrison.