I have also played a few times. I now realise Tradition is the only way to go, which is a shame as 150 turns into my latest attempt in a 4 city Liberty game I have great library and the pyramids, fantastic roads infrastructure etc for a low population. I struggled with happiness and didnt build an army yet. I planted the scientist from finishing Liberty and even now the science is lower than the city population score in Tradition.
Tradition would always beat Liberty on science, especially midgame, no doubt, but if you want to play 4 cities anyway, I don't know why to go Liberty.
I would say Liberty is faster to 3-4 city national college, due to faster libraries and free settler, but later slows down significantly in terms on science until around plastics.
You really need to plant more cities, to benefit from Liberty, either after 3city NC, or later, but burning GE finisher for NC - pre t.100 aim for at least 7-8, and a few later.
About road infrastructure - if your capital is not pop7, forget about building roads, than connect other cities with a rule - number of tiles with road less than expansion population. Otherwise it is too costly if that 1 more happiness does not repay it.
I went tradition first try only because I have discovered only 3 luxuries, in fact there were more available.
In this specific case however Liberty is a viable choice, as you have enough food everywhere, to minimise impact of no free aqueducts, you swim in faith and have guaranteed religion and you have plenty settling locations and difficulty level is low enough to guarantee Notre Dame. The other reason Liberty can work here is that there are quite some very productive tiles to settle mountainside.
While you cannot rely mostly on population in your expansion, liberty science game puts emphasis on science from flat yields - trade posts, specialists (while generating more great specialists) and multipliers not dependent on population - namely observatories and universities..
