OK so I tested both sites out and here's what I found:
Gold city:
I went WB-Lighthouse here and on turn 121 it was size 4 and ready to start spitting out settlers or infra (library probably). Here's some pros and cons:
Pros:
1) This is a stronger site overall, no question about it, 3 food and the gold which serves well for both production and commerce. Once it's up and running this city is a big boost for a long while.
2) The happiness boost was noticeable. The cap and rheims still need to be whipped/ recover from whip extensively and that extra gold makes a big difference. It saves hammers as well as you don't need to build, say, city defense in Rheims etc...
3) It doesn't need the worker straight away. I'm convinced that the best move atm is to get rheims to build a 2nd worker at pop 2 (it has to stagnate a bit otherwise it gets unhappy too quick). This worked out super well as we seriously need to get worker turns into the cap (hills mined, corn roaded etc...). As a result, the cap ended up well improved and the 2nd worker from rheims came out just in time to improve the gold. I felt that I wasted far fewer worker turns going this route.
4) We get to tech writing before AH, which seems like a good move given the importance of trade routes.
Cons:
1) As you will see, it takes a decent amount longer to set up than the Pigs fish city, but I feel it will make up that difference pretty quickly by weight of productive tiles.
2) Not as big a health boost as pigs fish city
3) it probably needs a monument and another wb as well not far down the track.
I then tried out the pigs fish city. It got set up super quick compared to gold (T107) but I felt that were a lot of sacrifices made as well.
Pros:
1) Gets set up super quick. WB comes from cap, worker improves pigs and hey, presto you're done.
2) No need for monument, lighthouse can help but isn't strictly necessary.
3)Extra health from pigs helps a bit
4) Possibly the best route to get a quick GS.
5) Has possibility of building exploratory WB instead of cap, freeing up some cap hammers.
Cons:
1) I actually struggled to find anything to build here when the city is founded. It has to grow so I really only saw the possibility of an exploratory workboat or a lighthouse for plus 1 food. Neither give huge benefits.
2) Once the city did get set up, I had a feeling of, alright, now what? It's pop 2 and only really has the choice between building a worker or settler at 2 pop. Or growing up to pop 4 on coast tiles and then whipping something out. Neither of these felt all too powerful. This is a low investment city, but it's not very strong...
3) Worker turns here feel a bit wasteful. To begin with we have the option of delaying the settler by 4 turns to pick up the worker then go back. In which case we delay the settler (obviously
) and we lose hammers to decay. Or we can whip the settler and leave the worker stranded on the island, forcing us to make a 8 turn round trip with the galley and severely delaying improving the pigs. Neither of these choices are pleasant. Furthermore, the worker gets tied up with improving the pigs (and possibly desert hill if we choose) which leaves the cap way behind in development.
4) I really missed the gold happiness in both orleans and paris here. It was very noticeable.
I think the biggest plus of the pigs/fish site is the possibility of getting the 4th city settled far earlier or having an early GS coming from here and freeing up the cap to build and whip units/wonders. The downside of the GS plan is that it means that this city will have basically nothing else to contribute to the empire. The gold city could also get our first GS, slightly later but it would have more hammers and food surplus to contribute in other ways as well.
Between the two sites, I think we need to decide on an overall strategy and that will dictate which site we should go for.
If we want to set up the empire economically, with a strong foundation by simply settling the strongest sites first, then we go with the gold site.
If we feel that we either need the next settler out super quick, or the 1st GS out as quickly as possible and are prepared to make sacrifices for this, then pigs fish it is.
My personal opinion:
With no real AI pressure on us to settle cities as quickly as possible, and no great use for an early GS. (Nothing to bulb, he could build an academy but if we want extra early research so bad we can just settle the gold site
) I feel that the gold site is the way to go.