I've done a bit more work on the maths, and come up with
these graphs. They show how long growth takes in turns with different average food production per population (between 2.5 and 4 food produced per citizen). For BE I'm assuming a grassland or equivalent city tile, so food 4 base. They illustrate that BE cities grow crazy fast early on, but then grow very very slowly as the get bigger. MUCH more so than Civ V BNW, where growth rate stays fairly linear from the teens onward if you can maintain a good food production per population.
There are a few more things that skew the Beyond Earth vs the BNW growth:
1) BE city tiles are 2 food + tile yield (BNW is almost always flat 2). So you likely have 4 food on the city tile.
2) BE has trade routes providing food and production pretty much straight away. The production is relevant because it also allows quicker building of e.g. vivariums. But trade routes provide a relatively flat amount of food - it doesn't scale up anywhere near linearly with foodbox size
3) BE has an outpost growth period, but this also allows workers to get a head start on improving tiles.
3) BE has farms and biowells that will generally provide more food per farmer than BNW.
4) Aqueducts and equivalent are the only things that really scale completely with city size. BE gives a pretty easy 10%, but getting more than that requires a fair bit of time and particular tech paths.
5) The ability for each new citizen to contribute to a food surplus pretty much drops somewhere between size 10-18 when you start to really run out of 3+ food tiles.
6) So BE has more food hanging around, but most of it is flat food bonuses that disproportionately speed early growth compared to late growth.
What this all means is that BE cities explode out to about size 10 in record speed, and then start to hit a massive growth wall. Which is pretty much exactly what you would want if you're going wide, but really bad news if you're going tall.