In this research note, the US-based Open Philanthropy Project discusses whether animal welfare might be helped or hindered by climate-focused reductions in meat consumption. For example, the note points out that meat types with a relatively low carbon footprint (e.g. chicken) are often from smaller animals (compared to, say, cows) and thus require more animals to be farmed and killed.
The note also discusses the potential trade-offs between livestock farming efficiency and the space available to each animal (e.g. it claims that free-range cattle may cause higher emissions than factory-farmed cattle).
Read the research note here. See also the Foodsource building block What is animal welfare? and the FCRN report Animal efficiencies, animal welfare: either/or, or both/and?