While it's true that cities all follow the same growth rules, they won't all have the same starting point: when you create a map, there will always be a few bigger cities and quite a lot of small towns. Since you'll probably serve the bigger cities first, those bigger cities will get even larger before the small towns get a chance to grow at all (since I think that transporting passengers/mail/goods to and from a city leads to higher growth -- is this right?). So there will always be quite a big discrepancy between the larger cities -- which will have many attractions and amenities -- and the smaller cities, which won't.
So I think that 'variable growth' is built into (a) the map creation and (b) the way you build your network, so having the same growth rules for all cities is probably the right approach.