When im playing Poland i mix Tradicion and Liberty, add to this Oracle and I can go Tradicion at normal speed but get free stuff from liberty as my UA perk. Good enought.
Piety, i have mixed feelings about Piety alone, since it provides no culture, and religion have synergy with more cities -> more shrines -> more double faith, and possibly more pantheon like tears of gods or oral tradicion. For Piety i would mix it with Liberty at least to collective rule just to pull out enought cities and shrines.
As for going Tradicion and Liberty on anything else, i think it is counterproductive since you mess with timing. You get free stuff, but not in right time. Tradicion opening postpone free settler, and even more free worker, and this worker is important! Even when you complete Tradicion it will be in the moment when you should have aqueduct built already.
And there are alternatives, instead of messing with liberty you can go just pure tradicion and get patronage and consulates and befriend every CS you can find on map.
Mixing tradicion and liberty opening you are messing with yout laiter stuff, harder time to fill rationalism or aestetic.
As for what is better Tradicion vs Liberty it really depends on civ, starting location, neighbourhood... there is no easy answear. Also at higher difficulties AI is cheating in every aspect and if you give it a time it will fil every spot on the map including island in the middle of the ocean, so there is just no time to start tradicion.