Bates, do you always have to ask difficult questions?? (That was rhetorical - I already know the answer.) That's just one of those Pandora's box-type question. It's also one that many heathens will not touch, because it often ends in nasty, bitter infighting.
The differences may seem very subtle, especially from an outsider's point of view or from the point of view of one who has not seen both varieties in action (i.e. most North American asatruar). I can assure you, that the end result of those subtelties are not so subtle.
The way I like to think of things is this: Asatru is a recreationist faith. Old Tradition is following an unbroken tradition. That about explains everything that comes after.
Some of the subtle differences are:
1. In North America, most asatruar follow the Gods and Goddesses, but forget about the landwights, spirits, alfar and jotuns etc. In Scandinavia, the focus lies equally on all those groups.
2. If you were to draw an axis and put the beginning of it at Old Tradition, and Wicca at the other end, those of us raised in Scandinavia generally place North American asatru somewhere in the middle of the axis. That is becasue N/A asatru focuses more on magical aspects, and it often mixes in new rituals and practises (by virtue of being recreationist, see below). Where Old Traditionalists see runes primarily as an alphabet with magical uses, asatruar often see runes as magical symbols that can also be used as an alphabet, for example.
3. Many of my asatru friends feel that it is an incomplete faith, because we cannot recreate all steps of it. Therefore they must create some new rituals etc or borrow from other religions, such as wicca, to fill in the gaps. Old Traditionalists like myself do not feel it is an incomplete faith, as it has functioned just fine w/o new rituals etc all these years. Because it is a faith that has been carried on through oral tradition, there is not much written about the old traditions in the first place, and what is written, has not been translated to English. The end result is often, that traditions that people in North America think do not exists, actually do exist in the old countries, but hidden from Anglophones and so on, so they substitute with other rituals and traditions. Those of us who were raised in the faith try to point out that those things do exists, but sometimes people just connect better with those new rituals and traditions. Neither can then be said to be "incorrect", just different from oneanother. We're still striving for the same end result.
Basically, Bates, it is like the Christian church having different denominations, the Moslems having Sunnis, Shiite and so on, the Bhuddists having Mahayana and Hinayana etc., etc. It is all one and the same faith, but slightly different. The basic idea of both is to respect others, and that includes respect for both types of heathenism. The difficult part comes in when someone says they are Odinist, because to many, Odinism is a separate religion, while to many others (and certainly to outsiders) Odinism is a branch of asatru.
Hope that sheds some light. Obviously there's more to it than that, but just to name a few differences.