Does rice milk or milk from grain-fed cows emit less methane?

[The Grand Nudger]

Are you saying chickens also emit a lot of methane? That's new to me.

Anyway, where are you getting your information from?

OFC they do.  What you've been focusing on is methane from enteric fermentation in the stock, and ruminants like cattle, elk, bison, sheep and deer certainly produce more of that.  I'll give you some envelope numbers for lifetime methane emissions in cattle, pigs, and chickens.  200, 10, .5 respectively.  Then you have to consider density.  1/10/500.  Then...and largely because we've included chickens in this comparison, you have to measure their lives.  Meatbirds are slaughtered at eight weeks, you get, on average, three runs per season.  Pigs, 6 months - so two, or thereabouts.  Cattle, one and a half to two years.  So, from enteric fermentation in the guts of each alone you could assume that an acre of cattle will produce 200lb of methane, and acre of swine will produce 100-200lb of methane, and an acre of poultry will produce 250-750lb of methane..per year  This is determined by putting animals in respiration chambers for some part, or all, of their life cycles.  You'll see why that qualification is important in a minute.  

The majority of the methane released by swine and poultry, however, isn't from enteric fermentation, as large as those numbers may seem.  It's from manure management.  Litter piles and effluent pools.  The latter sets up the same issue as rice patties, btw, just supercharged.  Then...there are..ofc, all sorts of other waste products from each type of op and all of the specific and individual inputs.  Some feeds and some feed producers (and retailers) are better than others, and this is variable by region and the size of the producers wallet.  Ultimately, this is why the method selected has the biggest effect on all byproduct production.  It's also why it's practically impossible to give a set of numbers for each that will hold on every op.  Differences in methods combine with differences in local conditions to wildly skew any of these numbers.  

Just looking at the envelope math you might, for example, ask yourself how cattle emit more methane overall than chickens even though an acre of chickens is easily capable of producing more and much more methane just from respiration than an acre of cattle.  That comes down to season and day length as well as land use and land use capacity.  Basically, cattle and pigs can more easily overwinter so they have a wider geographic range, and they grow to marketable weight slower, so fewer production runs are squeezed in even where local conditions are amenable to all three.  Then, on the accounting end (ie, as a consumer - you) the totals are based on something called dressed weight and dwr - which is different between locations, different between species, different between breeds within species, and different even when all these things are equal between producers.

In general, comparisons between them coming from a point of advocacy make hostile assumptions about the species or breed or producers or regions they wish to see reduced or eliminated, and generous assumptions about the breed or species or producers or regions they wish to see promoted.  In the process, all of these extremely relevant factors are ignored.  This allows us to say that...hypothetically, some versions of producing some crop or some livestock could be better than another, but we shouldn't believe or take that to mean that this is what we'd actually find if we hauled our own asses down to the farm and checked those numbers against the reality of production as is.  

In general, and hypothetically, you'll get the best numbers -specifically with respect to environmental concerns- out of combing all three in an aggressive mob grazing scheme.  The benefits here are largely not in any reduction to the methane from enteric fermentation (you can see an increase on that front) but in doing away with manure storage, the efficiency of land and input use, the reduction of pests and disease, decrease in labor and machine work, and increase in soil health, fertility, water retention, and vegetative mass.  Combined with no till grain and pasture management it's one of the only reliably profitable ecological farming loops - especially at scale.   

(I do grow poppies btw, they're called Jimi Hendrix. We do fish, poultry, mixed veg, herbs, and cut flowers - if they'd hurry up and legalize it I'd probably abandon all of that and grow weed. I certainly -do not- currently grow weed....officer. We're surrounded by tobacco, hay, grain, cattle..and, ofc, thoroughbred race horse nonsense.)