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I'm an undergrad law student at Oxbridge and I want to move to the US in the future (Canadian citizen). I currently have an offer with a leading UK firm which is V50 in the US. I have been given all manner of advice, including doing a JD, doing an LLM, or accepting the job offer. Would appreciate any thoughts on which road to take and which schools to apply to.

JD
Advantages: clearer pathway to a job
Disadvantages: cost, time, don't want to do law school for another 3 years, unclear if I'll get into a good law school

LLM
Advantages: time
Disadvantages: LawyersLosingMoney; seems like LLM graduates rarely get hired

Take my offer and lateral later on
If I take my offer, I will do a half-year Law Practice Course (LPC) and a 2-year training contract before becoming qualified in England.
Advantages: LPC is paid for by the firm, getting paid during the training contract
Disadvantages: pathway to the US as a lateral is not at all clear, my firm doesn't offer US secondments

If you are young, I'd seriously consider taking the job and seeing how you like it. There are some pathways for foreign lawyers who have practiced to later get an LLM and sit for the bar (I'm thinking of NY), but there are others. Someone correct me if I'm wrong, but you may not even need an LLM to sit for NY's bar exam (i've only heard this from one person and have no clue if it is correct).
Doing an LLM now seems like a waste. If you are going to the US right away, I'd just do the JD. The JD is the only secure way to jump into employment, but honestly, you'll be taking a 3 year hiatus (losing salary and paying tuition) and there's a potential future where you practice with a magic circle firm for 5 years, and then do an LLM somewhere in the US and work in NYC.
If your goal is to work in Atlanta or Houston or Chicago, I'd do the JD.
I still think the best option is to take this offer you now have in hand and see where it takes you. I love the US, but there could be challenges for you down the road, and if you hate London (which I'm guessing your firm is there), move out to Staines or something, or ask to transfer to the firms other locations within England & Wales.
I seriously considered doing the conversion GDL, but I really wanted to come back to the States (I'm an American and all my family is here). Additionally, I'm sure you're also aware that the UK's salaries are lower, but you make up for that in other ways.
None of your choices are bad, but being an oxbridge grad with a 2:1 or something and on a barristers pathway with a magic circle firm ain't too shabby at all. Lastly, you can always work a few years and then go do a JD, it isn't like you're precluded from doing so after working for a couple years with an LLB. So no harm in waiting a bit and seeing how it goes unless you're absolutely miserable.
Best of luck.

Agree with the advice to take the job for now from a career standpoint. If getting back to North America is more important to you, then a JD makes sense, but you'd have to stomach some career/immigration uncertainty which won't clear up for several years. LLM is the worst of both worlds and doesn't make sense until you've been practicing for a while.

I'd consider applying to some JD programs now to see what your options are. Or even just write the LSAT. Then you'll have much more concrete information about what that side of the fence looks like.