What defeat of regular Army forces versus natives was worse?

Isandlwana based on the colonial history of the British Empire (long history of stomping wogs).

Isandlwana was a much larger engagement than Little Bighorn.  

That said, it's a pretty even split IMO.  

Brits inflicted much higher casualties 
but they took a higher % of casualties 
The Sioux has greater technological parity with the US.  The Brits lost to guys (albeit a shitload of them) with spears.  

Id say that, man for man, the Brits performed better than the US.  But it's an opinion I'd have a hard time defending too ardently 

Isandlwana because it shocked the empire that was seemingly undefeatable

In the grand scheme of things? Isandlwana.

Note, however, that all it did was piss the British off, and they proceeded to curb stomp the Zulus, ultimately annexing their nation. Later battles were ridiculously one-sided, like the Battle of Gingindlovu, where the British lost 11 soldiers and the Zulus lost nearly a thousand.

If dealing with the natives, is the Martini Henri much of an improvement over the 1873 trapdoor Springfield?

Faster to reload, at least 

I wonder what the bayonet and rifle length difference is between the two rifles?

Only as long as you have ammunition!

Oddly enough I did a major research project on that very topic in college. I really enjoyed studying engagements where one side had a modern day army (rifles, arty, cavalry, telegraphs, etc), and the other more primitive (spears, swords, clubs, shields, loincloth, etc). The late 1800's is full of battles of this nature. From the Indian Wars of the US, to South Africa, to the South Asia Frontier of India, to the North African campaigns. China. Etc, etc.  

The two larger battles I focused on were Isandlwana and Little Big Horn. The discussion and debate on tactics and "what if's" is never ending, really. But in terms of being "worse" and having a larger impact on the losing army and country, Isandlewana was by far a deeper wound to the pride and politics of Great Britain than Little Big Horn was to the United States.  

Isandlwana could have been won, or at least a draw. Same with Little Big Horn. The glaring difference is the Chelmsford split his army before the battle and prior to the intelligence of "where and when", where as Custer made his blunder as the battle was unfolding right in front of him per say. The obvious mistake they both made is that they split their force in the face of an unknown size (and location) of an impending enemy. There are many other variables involved. But to keep on topic: Isandlwana was "worse".

Etc, etc, on and on.

How are the Indians doing nowadays?

Little Big Horn was foolishness on Custer's part: disobeyed orders, divided his forces in the face of Superior numbers?, refused to listen to his scouts.
The trooper's rifles in a few instances fell victim to environmental problems - corrosion from damp leather cartridge boxes caused a number of rifles to be unable to eject spent casings. Not a happy outcome facing a large hostile force.
Son of the Morning Star* gives a pretty good account of the circumstances comparing as many available accounts as possible.
Interesting tidbit was the Cheyenne counter attack included some women as fighters. One for the revisionist history folks to chew on!

* Son of the Morning Star was the name native Americans called Custer.

I'm saying LBH.
The Brits were attacked at Isa and Rourkes drift, the 7th Cav did the attacking.

Isandlwana by a mile, why is this even a question?

If you're talking miles, "Bearcoat" Miles was to arrive at LBH a few days after the battle.

The Martini-Henry is 49 inches long, 68 with the bayonet.
The Trapdoor rifle is 52 inches long, 70 with the bayonet.
However, Custer's men had carbines, which are 41 inches long, and I don't believe bayonets were part of the trooper's equipment.

The M-H is a mite faster to reload (at least for me), but, like the Trapdoor, had issues with cartridge case failure on extraction. When your single-shot rifle gets turned into a club / spear by a jammed empty, the M-H is the clear winner over the Trapdoor carbine, but the 7th Cav troopers also carried Colt revolvers, which 24th Foot did not have (except for officers).

In any case, the vast majority of the LBH engagement was well outside of bayonet / revolver range, unlike Isandlwana, where the Zulu had to come into assegai range (arm's length).

Some of us are doing fine, thank you very much.

I can't prove that any of my direct ancestors were on the battlefield that day, but the Rosebud and Yankton were both present then. I like to think that they played their part in ending George Custer's presidential ambitions.

I have to hand it to ol' George, he went down as a warrior, not groveling on his knees like a dog. How many presidential wannabes today would take to be field in combat against their enemies?

Quite a bit in this case US Cavalry was using carbines, Brits were using full length rifles. US Infantry Trapdoors are as long as a Martini . Carbines have no bayonet provision, and the Cavalry usually left their sabres at home when in the field.