As someone who is willing to spend on a western MBA/LLM for the sake of settling down there, does it make sense to go for a US Masters or should I try for countries like Canada, UK, or NZ?

There are many Indian lawyers, who have switched their jobs - took MBA in the US, and emerged successfully. Aprt from the big law folks, there are many who did LLM, and working as Immigration & Familiy /Commercial Attorneys in smaller cities; But those were in the 1990's to 2010 era (Pre-Trump) Even thou it looks like the anti-immigrant rhetoric has reduced and chances of getting a Work Visa and Green Card has increased. Is it worth spending so much to go to the US?

How are other countries - Canada/NZ?

A lot of top MBA programs in the States are STEM certified (Sloan, Haas Berkeley , ,Kellog etc) thereby giving you the opportunity to stay and pay back your loans vs a LL.M. If you manage to get into HBS, Whatron, Stanford GSB, Booth etc. then in all probabilities you will get a permit. MBB and top notch IB firms hardly get any of their sponsored visa applications rejected, also if from a Top 10 b school then the kind of opportunities you would get is unimaginable as the elite b school tag has that pull. So, if you can get into a top US b school, then it's a no brainer.
But, the LL.M scenario is quite different. The legal market there is already saturated and getting a well paid job would be much more difficult with a LL.M (but you would have good shot with a T14 JD). So if your primary aim is to settle in US, MBA is the best route possible. Plus if you are that much into law then there's the JD/MBA route, but that costs much more plus another year. Many elite dual degree programs are out there such Wharton, Columbia, Northwestern etc.
At the end of the day, it's your call to make. But in my opinion, MBA remains a good route if you make it into the top B schools. All the best for the future, may God bless you.

Like 1.1 said, MBA is the best possible route to immigrate into any country. LL.M on the other hand, simply does not open up many doors for you except in academics. However, if you don't happen to be from a T1/T2 law school (UG) then the LL.M might compensate for that lack of the brand name, but still you can make it into good chambers/T1 law firms without a LL.M as a year or two of work experience is good enough to make the shift. So my advice would be to go for a LL.M abroad only if it solves a particular purpose for you, but if you want to immigrate to any country whatsoever, then MBA is the best degree out there owing to its flexibility.
In regards to Canada, MBA is perhaps the only respectable route (barring tech folks). The legal market is much more worse than in the US. Do not even think of a LL.M in Canada, unless you want to work in immigration clinics. NZ isn't any better I guess.

I have many friends who took a hefty loan for a MBA and had to come back home empty handed; the American dream is over mate and its all thanks to the green card lottery system. If you don't happen to be from a rich background or have good enough savings, then don't venture out into the US with big dreams, chances are that you will be disappointed. Furthermore, bhai agar kuch gar bar huwa toh loans kon bharega? Can your parents support you in that case? Do you have enough money in the bank in case things don't turn out well? Think carefully bro/sis, kuch anon "HaRvArD/WhArTon/StAnFoRd" fans will try to sell the dream to you, it sounds good on paper lekin sachai kuch aur hai. Not many make it to the super-elite ones, and even some of them who do run out of luck many a times (the shitty visa system). Many Indians are trying to avoid going to US for higher studies, even though policies MIGHT become more immigrant friendly, but it still is a BIG BIG risk. And let us not talk about LL.Ms, the scenario is even more bleak. You would not believe this, but I have seen my neighbours son return to India after a NYU Stern MBA, he was an intelligent NIT W grad with solid 3 years work experience. There are many such cases, just google it. Not saying that you cannot get a job, but the risk is high.
If you want a MBA that badly then get one from IIM/ISB/SPJAIN/FMS/JBIMS etc. Many people do a 2nd MBA from abroad, its not a big deal. But if you get good scholarships, then there's no harm in going, at least exposure toh badhiya hoga and if you get a job tabh life is set. For LL.M, its better to opt for affordable European colleges- light on pocket and good academic exposure. Think carefully mate, try connecting with real life Indian law school grads pursuing/have pursued their MBA/LL.M in USA, you will find plenty of them in Linkedin. Don't listen to anon guys on LI.

Just how many people at top 10 US MBA programs return back to their native country? Yes, some people do come back empty handed but anyone who knows to network and is not dumb as a koala bear will find some way or another to get a job. Plus, its not as if everybody gets a job in USA itself, if you go through the placements statistics of any Top B-School then you would come to know that people are recruited all over the world. You would find plenty of Harvard/GSB/Wharton/Insead/LBS alumni working across the globe with respectable salaries. And yes, good companies hardly get their sponsored visa applications rejected, and the B school tag does play a significant role in such applications.
No one is selling you the dream, but if you make it to the good B schools, the brand value and the opportunities associated with it unimaginable. You would be taken seriously by people across the globe (as long as you aren't as stupid as a Koala Bear that is), and in all probabilities you will have it much easier when it comes to getting a respectable job. So if its a top MBA program, one should go for it but once again, to each his own, it depends on the individual's circumstances.

It does. Folks here seem to be unaware of the hiring spree in the US which started end of 2020 and continues till date. Every Indian LLM from a decent school graduating this year has got a job with a Big Law firm - never seen before situation. Will last another year but will probably be back to normal 2023 onwards (i.e. jobs will be difficult to come by for LLMs).

My Dear Dude

Nobody is telling that there is lack of Big Law jobs in the US. US has a lot of jobs for almost every foreign student who studies there - MBA's and MS folks do get a ton of offers.

Canada and New Zealand doesn't have enough high paying jobs. People who leave well paying jobs in India end up becoming Lawyers at small immigration clinics and Tim Hortons. But staying back in Canada/NZ is easy because they have Liberal immigration laws.

But guess what?

Even if you have a ton of job offers from AM100 - whether you will be able to work in the US is like a lottery. Because to work in the US, you need immigration clearance or work permit.

American immigration is very restrictive these days. A lot of Indians get jobs in the US - but are still forced to come back because of immigration issues. H1B is very difficult to obtain. US Greencard Citizenship is impossible for Indians (see the backlog)