In this analysis I will consider the effect of the Burgundian team bonus (Relics additionally generate food (at the same rate as they generate gold)). I will not consider other civ bonuses (e.g. Chinese extra food on farms or Teutons cheaper farms).
It's commonly known that a relic is roughly equivalent to an extra villager mining gold (1.15 villagers with the Gold Mining; 1 villager with Gold Shaft Mining).
The Burgundian bonus adds an additional 0.5 f/s to the existing 0.5 g/s granted by a relic. However, miners work faster than farmers, and farms cost wood.
Because farms cost wood, the passive generation of food of Burgundian relics gives you a small effective amount of wood (e.g. if you had to recreate the food bonus using villagers you'd need to have a villager on wood, at least some of the time)
Under ideal circumstances (all upgrades; no villager bumping; no other inefficiencies) each Burgundian relic is worth an extra 1.3 villagers (i.e. a relic is worth 2.3 villagers instead of 1 villager).
Under realistic circumstances (no crop rotation; realistic gathering rates) each Burgundian relic is worth an extra 1.5 villagers (i.e. a relic is worth 2.7 villagers instead of 1.2 villagers)
So under realistic circumstances, 5 Burgundian relics are roughly equal to 7 farmers and half a lumberjack (and 6 gold miners) for a total of a little over 13 villagers.
A rule of thumb: a Burgundian relic is worth 2.5 villagers per relic