Both are minority destinations, and that is the fact that gets lost. Almost nobody went to either. The overwhelming majority of the Norse dead went to Hel, and the overwhelming majority of the Greek dead went to the undifferentiated shades of Hades. Valhalla and Elysium are exceptions carved out of a default, and comparing them without saying so gives the impression that these cultures expected a good afterlife. They did not.
The entry criteria are the whole difference
Valhalla admits by manner of death, selected in advance. Those who fall in battle are taken, and the valkyries do the choosing on Odin's behalf — which means the selection happens before the fighting, not after it. This is recruitment. Odin is assembling the einherjar, a standing army to fight at the end of the world, and he needs numbers. The famous consequence, that he stirs up wars to increase the intake, follows logically from the personnel policy.
Elysium admits by birth, favour or, much later, merit. The oldest Greek description does not mention virtue at all: Menelaus is told he will go to the Elysian plain because he is married to Helen and is therefore the son-in-law of Zeus. That is a family connection. Hesiod's Isles of the Blessed hold the heroes of a previous race, which is a matter of when you were born. Only considerably later, in Pindar and then in philosophical and Roman literature, does a moral or initiatory criterion appear, with the requirement of repeated blameless lives.
So: one system selects for how you died, the other for who you were. Neither selects for goodness in its earliest form, and both were later moralised — the Greek one much more thoroughly.
And the accommodation could not be less alike
Valhalla is a hall with a great many doors, roofed with shields, a wolf hanging at its western entrance. The daily routine is documented: the einherjar fight each other all day, are killed, get up, and drink in the evening on the flesh of a boar that regenerates and mead from a goat that stands on the roof. It is an eternity of the best day of a warrior's life, on repeat, with the explicit purpose of keeping the force in training.
Elysium is a landscape. No snow, no storms, no hard winter, a west wind blowing off the ocean, easy living. The later Roman version develops it into a region with groves, athletics, music and reunion. Nothing happens there, and nothing is supposed to. It is a retirement.
That contrast is worth sitting with. One culture's ideal afterlife is permanent employment; the other's is permanent leisure.
The Norse arrangement is more crowded than usually reported
Three corrections to the popular picture.
First, Odin does not get all the battle-dead. Eddic verse states that Freyja receives half of those who fall, at her hall in Fólkvangr, and that she chooses first. A great many summaries of Norse religion omit this entirely.
Second, drowning is its own jurisdiction. Those lost at sea go to Rán, who takes them in her net — a real concern for a seafaring society and a destination nobody chooses.
Third, there are further options in the sources, including a hall for the dead of certain families and, in some material, an expectation of remaining in the burial mound. Norse afterlife belief is plainly not a single system, and the tidy scheme most readers meet owes a great deal to one thirteenth-century Icelandic author's effort to organise it.
Why "die in battle to reach Valhalla" is oversold
It is in the sources, and it is also a modern slogan. Two cautions.
The evidence for what ordinary Scandinavians expected comes mostly from grave goods and from poetry composed for aristocratic patrons — and the poetry that describes Valhalla in most detail is memorial verse for kings, where placing the dead lord in Odin's hall is a compliment with obvious political utility. Whether a farmer in Jutland thought the same way is not recoverable from that evidence.
And the modern deployment of the idea has a history worth knowing. Valhalla was heavily used in nineteenth-century Romantic nationalism, and elements of Norse afterlife imagery have since been appropriated by movements the sources give no warrant for. Reading the material carefully includes noticing who has been using it and for what.
The Greek case has the same problem in reverse
Elysium was moralised over time, and the direction of travel matters. As mystery cults and philosophical schools offered better outcomes to initiates and to the just, the blessed afterlife expanded from a handful of relatives-by-marriage into something available in principle. By the time of Roman epic it has an organised geography, and by the time it reaches medieval Christian imagination it has supplied a good deal of the furniture of paradise.
Reading the earliest Greek material through that later development is the single most common error in this area, and it makes archaic Greek religion look far more reassuring than it was. See the underworlds compared for how the general destination worked.
Connected pages
Valhalla, valkyries, Freyja, Odin, Hel and Helheim on one side; Hades, Tartarus, Persephone and Charon on the other. For the Irish comparison, which behaves differently again, see the Norse and Celtic otherworlds.
Who was eligible, who knew, and what the graves suggest instead
Could a woman reach Valhalla? The sources do not address it directly, which is itself informative — the hall is described in terms of a war-band and the criterion is death in battle. Some later saga and legendary material complicates the picture, and Freyja's claim on half the slain has been read by some as opening a route, but anyone stating a firm answer is going beyond the evidence.
Is Elysium the same as the Isles of the Blessed? They start as separate ideas and converge. The Elysian plain in the earliest account is at the ends of the earth; the Isles of the Blessed are islands in the Ocean holding the heroes of the age of heroes. Later writers treat them as the same place or as adjacent districts, and Roman poetry relocates the whole thing into the underworld proper, which is where most readers meet it.
Do the einherjar know they will lose? The tradition is explicit that Odin is preparing for a battle he is fated to lose, and that he knows it. Whether the recruits know is not stated. That silence is one of the more affecting gaps in the whole corpus, and it is a gap, not an answer.
Which afterlife did ordinary people actually plan for? Grave evidence in both cultures suggests something more local than either literary destination: provisions, tools, personal objects, and in Scandinavia sometimes a ship — arrangements that make more sense if the dead were expected to remain connected to the burial place. Ritual practice and epic poetry are describing different things, and the practice is the better guide to ordinary belief.