Both cattle and sheep are ruminants, ie. they digest herbage and therefore produce methane. Sheep are not “worse”, it just that there are more of them in the world (20+ Million in the UK).
Most cattle in the USA are kept indoors and fed only on maize, to produce marbled meat. This is a cruel system. In many parts of the world sheep and goats are the only way to garner food from poor (often mountainous terrain). They have had a symbiotic relationship with these ovines for thousands of years. And hitherto it has been the same in the UK: sheep got protection from predators and supplementary fed during the winter, in exchange for wool and the meat of their offspring. Grazing animals can have really important environmental benefits in maintaining some wildlife rich landscapes. Its all complex and a question of balance. The nub is: intensive farming bad, extensive farming better.
The choice you have if you are concerned about climate change is “meat or no meat” and eat only a plant based diet. Its easily doable. That is the trend of consumption now in the West, for good or ill, not just because of the climate issue but one of personal health and aversion to animal cruelty and cost.
As I have said before I am from a farming background and understand all sides of these issues. My take on them these days is to tread lightly on the Earth in contrast to my past.
My favoured solution to all these problems is for townies who do not know where cheese comes from (!) is for them to starve themselves to death.
P.S. to produce most cheeses calves have to be killed (milk + rennet. Google).