In either case, you'd still need to massively reduce the population of said animals.
I mean, there are several scenarios. There's the "everyone turns vegan overnight" scenario. The "mind control everyone to reduce their meat intake gradually over the course of 20 years until they go full vegan scenario". And I'm sure there are other scenarios but let's go with these for the sake of this debate.
In the first scenario, there would be massive economic and ecological upheavals, not to mention the whole "abandon most of the animals to fend for themselves" scenario already discussed above.
The second scenario is similar to the above, but it'll be a gentler slope. Farmers will still just abandon their livestock or mush 'em up if they can't convert to other industries like leather.
Nonetheless, let us assume everything will normalize sooner or later and we now have a bunch of livestock who've adapted to the wild by going feral but otherwise, don't really bother us.
The question is, what's the environmental impact? Certainly, not having cows would mean far less erm, shall we say, bovine emissions. And cows do take a huge amount of grazing land.
But you know, most other livestock don't. Chickens and pigs take only a fraction of the land that cows require.
The question is, how much land is going to be needed for farming, to produce the same caloric output as we'd get from livestock?
And how about preservation of food? Like, meat you can deep freeze for years if need be. If supermarkets can't store veggies for weeks/months, imagine the waste that would incur. Most food will end up being slathered in preservatives because they can't just keep throwing them out if people don't buy them within a week or two.
And lots of problems beyond animal cruelty or farming land.
tl;dr, Going full vegan opens up a whole mess of problems which can be solved by having a BALANCED diet of meat AND veggies. Because meat eaters don't eat ONLY meat.