Aristogarian farm yields:
Grassland: 4(5*)

2(3**)

2***(2.5)

+1.5 specialist
Lumbermill on ancient forest:
Grassland: 3

0(1/2/3/4)****

2(3/4/5)*****

+0.5 specialist
This is for RifE, dunno if the yields were changed much.
River adds 1 to the farm, but 2 to the lumbermill (I believe this isn't true in vanilla FfH, as it only adds one to both).
* 5

with sanitation
** 3

with financial
*** Hammers come from population, this is assuming that the city is below health cap, and all food is used.
**** base

is 0, one with river, one with construction, one with optics and one with industry plus one if financial and >1
***** base

is 2, one with construction, one with optics and one with industry.
The lumbermill has better

yield in general, and worse

yield.
It has better commerce yield, but this comes late.
To calculate the extra specialist in: If we say that

=

(which it doesn't, but close enough to use), the aristogarian farm wins the commerce yield with 5(6) (or 7 with the Great Library), or it can go even with

. This gets better with floodplains (0.5 specialist extra and 0.5

), but worse with plains (same, reversed).
This means that the lumbermill isn't that much of an advantage, however, the extra health is.
AV, however, is wicked (pun intended, sorry).
Grassland aristogarian farm; AV style:
4(5*)

2(3**)

4***(5)

+3(4) specialist
This equates to (here Guilds is most likely required):
14(15)

/:research: (or 18(19) with the Great Library) 4

(financial) with sanitation using scientist.
2(3)

16

(financial) with sanitation using engineers.
Yes, that is the yield from
one tile.
Bonkers, completely bonkers.
This does require a low of health resource and management, but it's extremely powerful. This also makes for a turning point, in were aristocracy isn't needed anymore, as the specialist provides as much or more. God King capital, filled with farms, running merchants, will pay for pretty much anything. Abso-friggin'-lutely insane. There is a reason AV was nerfed in RifE (up to 1.5

per pop).