Interesting question. The 1936 version has almost nothing to do with the actual event and is perhaps best remembered because it gave David Niven the title for one of his immensely popular autobiographies, Bring On The Empty Horses.
I think I saw the 1968 version in the cinema (probably a re-release for Saturday morning matinees) and loved it at the time.
But I'm wondering which version would seem the most dated now, the old B&W classic Hollywood or trendy 1960's British retelling. Worth seeing both again to decide.
I have always depended on the kindness of Strangers - and the bastards let me down!

When in doubt, go with Errol Flynn

That's an interesting remark you make about the 1936 version being used to bolster US support for England who was fighting at this time. In 1936? I don't thing England was fighting anyone then, apart from small colonial conflicts, NW Frontier of India, etc.
I've never understood why most films are made, except of course to provide profit for the studios, so I don't think Warner were particularly concerned with supporting England in an unyet started conflict!

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Beyond the title and the genre subject matter, not really comparable IMO. The 1936 version hasn't the slightest relation to historical fact, while the '68 version is all about historical accuracy.
That said, the '36 film is better made and definitely more entertaining than the later version. That film's depiction of the Charge, accurate or not, remains perhaps the best battle scene in Hollywood history (I might put a few non-Hollywood scenes like Bondarchuk's epics ahead of it), Errol Flynn is in top form and the story's entertaining enough if you accept it as fiction.
"I shall tread uncommon wary and keep my pepperbox handy."

"Hollywood derring-do, which has the charge take place on the North-West Frontier of India"
Not quite. The 1936 charge takes place in the Crimea, but erroneously attributes the reason for it to a Northwest Frontier incident.

Depends what you want - Hollywood derring-do, which has the charge take place on the North-West Frontier of India, or historic reconstruction (reflecting 1960's values) filmed on location. Two totally different films.

If you want to know the real story of the Charge of the light Brigade during the Battle of Balaclava, what happened and why, the 1968 version.

I just watched both recently, and have been watching some Errol Flynn films since I was told to give him a chance (over Stewart Granger). Imo the 1936 exceeds this quite significantly.
I have seen Flynn's other action films and tbh I think they're OK but not gripping unlike Granger. I take exception to this though, this and his Elizabeth and Essex are one of the best, a 9/10 rating for me.

I have to agree about the cavalry charge, I cannot imagine that scene being replicated today with all the horses deaths and that of his friend, with a sword through the heart when he fell off his horse. The charge remindid me of the one in Attack on Titan, I can only think the creator was very much influenced by the 1936 film.

Well, unless you're a big fan of Errol Flynn, the 1936 film doesn't have a lot to distinguish it from a heap of other films made around that time.
I disagree.
Flynn's version is probably the best cavalry charge scene in any movie.
Very stirring stuff but as mentioned, made in California and looking like the Northwest frontier.
The B&W visuals are strangely much better than the color film of the 1968 moviethe costumes show up black and very strong.
It's an unashamed heroic action movie and Errol Flynn really did ride in the shooting of the charge.
Great stuff.

I just saw the 1968 version. It was nice. The battles were very anti-war in a good way and there were no dumb heroic actions that would degrade this to an action movie.
The beginning was a bit slow, but it showed the stupidity of England in that time (or at least of it's officers and beliefs)

Well, unless you're a big fan of Errol Flynn, the 1936 film doesn't have a lot to distinguish it from a heap of other films made around that time.