Ask what happens after death in these two traditions and you will get one straight answer and one that keeps sliding out of the question. The lopsidedness is not a shortfall in what survives. It is the result.
Scandinavian material sorts the dead into destinations according to how they died, and at least one of those destinations exists for a stated purpose. Irish and Welsh material has an elsewhere that is magnificently developed and is only intermittently about death at all — it is a neighbouring country, and living people go there and come back, which is the one thing no Norse dead man does.
The Norse arrangement is a posting
Valhalla is the part everyone knows and the part most often misdescribed. Its inhabitants are not being rewarded. They are being assembled: chosen from the battle-slain, housed, fed, and exercised daily in fighting that resets each evening, against a future engagement at the end of the world. The hall is a barracks with excellent catering, and its logic only makes sense because Odin has a war coming and needs numbers. Even the valkyries fit that reading better than the Romantic one — their name is about choosing, and choosing is a personnel function.
Around it sits a scheme of alternatives. Freyja takes half of the slain to her own field, which is a genuinely odd arrangement nobody in the sources explains. Those who die otherwise go to Hel, which is a place and a person and is not a punishment — it is simply where most people end up. The drowned are said to go to Rán. Poems mention halls belonging to other deities where their own receive them.
The important caveat, and it is a large one: this tidy scheme is much more visible in Snorri Sturluson's thirteenth-century handbook than in the older poetry, which is inconsistent about where the dead are and sometimes puts them in the burial mound rather than anywhere cosmological. Archaeology agrees with the poems rather than the handbook — Viking-age funerary practice is wildly various, with cremation, inhumation, boat burials and chamber graves coexisting in the same regions, which is not what a settled national doctrine looks like. Read the Norse afterlife as a scheme with a thirteenth-century editor and the sharp edges soften considerably. The Hel and Hades comparison works through the destination itself; the Valhalla and Elysium pairing takes the recruitment question further.
The Irish and Welsh arrangement is a country next door
Now the other side, and the first thing to fix is the map. The Irish síd is a mound — an actual visible monument in an actual field — and the Otherworld is understood as being inside or beyond it. Other routes are westward over the sea, or under a lake, or through a mist. What lies on the far side is not a realm of the dead. It is a well-run kingdom with kings, feasts, music, livestock, quarrels and marriages.
The clearest demonstration is Welsh. In the First Branch, a prince of Dyfed offends Arawn, the king of Annwn, and the reparation agreed is that the two men swap appearances and realms for a year, each ruling the other's territory, with Pwyll additionally required to fight Arawn's rival on a specified date at a ford. Annwn here has a border problem, a succession dispute and a diary. It is a foreign court, and the story is a story about honour between kings. Reading Arawn as a death-god and Annwn as a Celtic hell imports centuries of later assumption into a text that offers no support for it.
Irish material never settles on one name for the place; the labels it uses advertise pleasure, life or apples in roughly equal measure, and Tír na nÓg is only the one that happens to have reached English. It reaches them through two related story types, the echtrae or adventure into the Otherworld and the immram or voyage across the sea. Some of the dead are there. So are the Tuatha Dé Danann, who in the pseudo-historical scheme retreated into the mounds after being defeated, which makes the Otherworld a relocated former ruling class rather than an afterlife.
The time problem, which only one tradition has
Here is the genuine, non-trivial structural difference, and it is not a detail.
Irish Otherworld narrative is obsessed with mismatched time. Oisín goes away with a woman of the Otherworld, believes he has been gone a few years, returns, and discovers centuries have passed — and when he touches the ground of Ireland he ages into them all at once. In the voyage of Bran mac Febail, a returning crewman leaps ashore and crumbles to ash on contact, while the men in the boat learn that their departure is now a story old people tell. The tale of Nera runs the effect in reverse: a man spends what feels like a long stay in the mound and comes out to find almost nothing has moved.
The Norse afterlife has no version of this at all. The dead in Valhalla are simply there, on the same timeline as everyone else, waiting for a dated event. Nobody comes back to find the world has aged, because coming back is not on the menu.
That difference follows directly from the two conceptions. If the elsewhere is a destination, its clock does not matter. If the elsewhere is a place living people visit, the clock is the whole drama — it is the mechanism by which a visit becomes a loss, and the reason these stories are so consistently melancholy underneath the feasting.
Neither tradition judges you
Worth stating plainly, because both get retrofitted with a moral filter they do not have.
Norse sorting is by manner of death, not by conduct. A cruel man killed in battle qualifies for the hall; a decent one who dies of illness does not. There is a nasty shore in one poem where oath-breakers and murderers wade through venom, and it is a strong candidate for Christian influence on a late text, precisely because it is so isolated.
Irish and Welsh Otherworlds sort by invitation. You are there because someone summoned you, married you, abducted you or gave you a branch of silver apples. Merit is not the currency; attractiveness to an Otherworld host is.
Set that against the Egyptian weighing of the heart or the ledger-keeping of Indian eschatology and the contrast is sharp. Two of Europe's most famous afterlives run entirely without an ethical test.
Where the comparison is doing damage
Three warnings, because this pairing attracts more confident nonsense than most.
"Celtic" is not one tradition. Irish and Welsh material are separate literatures in separate languages with separate transmission histories, and merging Tír na nÓg with Annwn produces a composite that never existed anywhere. The Gaulish evidence, which is what "Celtic" originally meant, is archaeological and epigraphic and tells us almost nothing about afterlife belief. The single classical statement — Caesar's report that the druids taught that souls pass from one body to another — is an outsider's summary, likely filtered through what a Roman reader knew of Pythagoras, and it is thin ground for anything.
Both bodies of evidence are Christian-mediated, and differently so. Norse cosmology comes to us through Icelandic writers two centuries after conversion. Irish Otherworld tales come to us through monastic scriptoria, and in several cases the monks are visibly interested in the material for their own reasons — the voyage genre shades directly into Christian visionary literature, with the Voyage of Saint Brendan on one side of a boundary that is not always clear.
Tír na nÓg's famous shape is modern. The specific story of Oisín and Niamh, riding west and returning to a changed Ireland, takes its familiar form from a mid-eighteenth-century Irish poem, and much of the imagery English readers associate with it arrived through nineteenth-century translation and revival poetry. The underlying motifs are genuinely medieval; the packaging is not.
Follow-ups
Did Norse people believe in reincarnation? A few sagas contain a note that a person was "born again", usually attached to name-giving within a family, and the compilers sometimes add that this was believed in the old days — which is the tone of an antiquarian recording something no longer credited. It is present, marginal, and not a system.
Is there a Celtic Valhalla? No, and the absence is diagnostic. There is no Irish or Welsh institution that gathers dead warriors for a future battle, because neither tradition has an eschatology of that shape. Feasting in the Otherworld is hospitality, not readiness.
Which tradition's dead can be visited? Only the insular Celtic one, and freely — the mound is in the landscape and stories are full of people going in. Norse literature has the mound-dwelling draugr, and the encounter is nothing like a visit: it is a fight with something that should have stayed buried.