Here is my approach for tradition:
- shrine, scout, worker, GL, Oracle, Hanging Gardens (a must for tradition and GP boost). There is some deviation from that though.
My reasoning: when you aim for a tall empire, tech is on your side, because tech costs increase by 2% per city. If you have tech under control, you can start building wonders earlier and with aristocracy, you can gain about 1 production for every 6 production being generated at the city working on a wonder. This could be the difference of 1-2 turns. I also recommend founding a religion based on growth if you're going tall. Getting ToA would also help.
15% growth at capital + 10% growth from fertility rites + 15% growth from swords to plowshares + 10% growth from ToA = 50% growth rate and tall empire in a short space of time. Add hanging gardens for even further growth at capital. It will mean higher GP rate, faster tech speed and more production.
Keep in mind that pyramids and stonehenge also provide free GE points. However, this can be offset if you're aiming for finishing tradition and purchasing GE's with faith.
As for piety, if you're aiming to complete piety then stonehenge is somewhat pointless. Having a relatively wide empire helps for religion, unless you choose world pilgrimage to gain faith for every city with your religion as the dominant religion. Also, with my piety game, I chose heathen conversion mostly for the lols. It is very useful if you're going for autocracy. If you get over 10
, have a missionary at your capital, and you'll gain 2-3 troops every 5 turns or so.
As for honor, this is rather tricky. Although barbs will be less of an issue, honor obviously lacks development policies such as free settler and worker in liberty or increased growth in tradition. However, completing honor would help lower upgrade costs. Its happiness boost is best combined with oligarchy from tradition and a wide empire, as well as a large army. And warmongering is too risky in BNW. However, honor might help in very intense fights, offering at a 30% combat bonus to your troops with a nearby general and discipline. If you warmonger, you have to keep this sequence in mind:
1. Attack civ you wish to attack
2. Other civs hate you (some might tolerate warmongers instead).
3. wave of denounciations against you.
4. 30 or so turns later, everyone DoWs you.
Conclusion: I personally think tradition is best path for most civs in BNW. Anyone aiming for liberty should consider aiming tall eventually or face a huge tech cost.
Hope all this helps.