Well firstly you can’t really compare apples with oranges- a plant based whole foods diet is different from one which relies wholly on packaged and processed foods.
But yes, environmentally local meat is worse for the environment than even imported plants.
pubs.acs.org/doi/full/10.1021/es702969f
“buying local” could achieve, at maximum, around a 4−5% reduction in GHG emissions due to large sources of both CO2 and non-CO2 emissions in the production of food. Shifting less than 1 day per week’s (i.e., 1/7 of total calories) consumption of red meat and/or dairy to other protein sources or a vegetable-based diet could have the same climate impact as buying all household food from local providers.”
www.sciencedaily.com/releases/2018/10/181023110627.htm
“A new study provides a more comprehensive accounting of the greenhouse gas emissions from EU diets. It shows that meat and dairy products are responsible for the lion's share of greenhouse emissions from the EU diet.”
“The study found that meat and dairy account for more than 75% of the impact from EU diets. That's because meat and dairy production causes not only direct emissions from animal production, but also contributes to deforestation from cropland expansion for feed, which is often produced outside of the EU.”
“"People tend to think that consuming locally will be the solution to climate change, but it turns out that the type of product we eat is much more important for the overall impact," says IIASA researcher Hugo Valin, a study coauthor and Sandström's YSSP advisor. "Europeans are culturally attached to meat and dairy product consumption.”
Most of the soya imported into the U.K. from the Amazon is fed to animals:
www.wwf.org.uk/sites/default/files/2017-10/WWF_AppetiteForDestruction_Summary_Report_SignOff.pdf
“Today, protein-rich soy is such an important feed ingredient that the average European consumes approximately 61kg of soy per year, largely indirectly through the animal products that they eat like chicken, pork, salmon, cheese, milk and eggs. In 2010, the British livestock industry needed an area the size of Yorkshire to produce the soy used in feed. And if the global demand for animal products grows as anticipated, it’s estimated that soy production would need to increase by nearly 80% to feed all the animals destined for our plates.”
But even purely grass fed animals are problematic:
www.tabledebates.org/node/12335
This report finds that better management of grass-fed livestock, while worthwhile in and of itself, does not offer a significant solution to climate change as only under very specific conditions can they help sequester carbon. This sequestering of carbon is even then small, time-limited, reversible and substantially outweighed by the greenhouse gas emissions these grazing animals generate. The report concludes that although there can be other benefits to grazing livestock - solving climate change isn’t one of them.
www.google.co.uk/amp/s/amp.independent.ie/business/farming/forestry-enviro/blow-for-grass-fed-beef-as-new-report-suggests-its-part-of-the-climate-problem-not-solution-36209259.html
But at an aggregate level the emissions generated by these grazing systems still outweigh the removals and even assuming improvements in productivity, they simply cannot supply us with all the animal protein we currently eat. They are even less able to provide us with the quantities of meat and milk that our growing and increasingly more affluent population apparently wants to consume. Significant expansion in overall numbers would cause catastrophic land use change and other environmental damage. This is especially the case if one adopts a very ‘pure’ definition of a grazing system, the sort that grazing advocates tend to portray, where livestock are reared year-round on grass that is not fertilised with mineral fertilisers, receiving no additional nutritional supplementation, and at stocking densities that support environmental goals.
link.springer.com/article/10.1007/s10584-020-02673-x
“Grazing systems emit greenhouse gases, which can, under specific agro-ecological conditions, be partly or entirely offset by soil carbon sequestration. However, any sequestration is time-limited, reversible, and at a global level outweighed by emissions from grazing systems. Thus, grazing systems are globally a net contributor to climate change.”