What makes the Ulfberht swords special (not necessarily "great") is that about 1/4 of them are made with high-carbon low-slag steel, some of which are very high in carbon. It has been suggested (quite reasonably) that these swords are made from crucible steel imported from Asia (either Indian crucible steel, i.e., wootz, or Central Asian crucible steel, i.e., pulad/bulat). It has also been suggested (rather problematically) that these crucible steel Ulfberhts (i.e., possibly crucible steel Ulfberhts) are the original high-quality swords that the Ulfberht "brand name" described, and the other ones (usually with differently spelled inscriptions) are inferior copies/counterfeits.
Overall, the Ulfberht swords can be divided into 4 groups, each roughly equal in numbers (i.e., each group is about 1/4 of all Ulfberht swords):
+VLFBERH+T: All-steel construction, with high-carbon low-slag steel. Many of these swords have carbon contents of well over 1% (up to about 1.2%). Others have carbon contents as low as about 0.5%, and some have much variability in their carbon content. It is possible that the variation in the carbon content, and perhaps the low overall carbon contents of some of the swords are due to decarburisation during forging. It's also possible that the variation in carbon content indicates that some of these blades were made by welding together steels of different carbon contents.
Mostly +VLFBERHT+ (and some variants): Pattern welded construction with steel edges on an iron body, quench-hardened. The steel edges typically have carbon contents of about 0.5% to 0.8%.
Various spellings: Pattern welded construction with steel edges on an iron body, unhardened.
Various spellings: Iron swords.
Williams (2012) classifies these swords into 5 groups; group 1 above is groups I and II of Williams, and groups 2 to 4 are Williams' III to V.
Looking at the styles of guards and pommels, the pattern-welded Ulfberhts appear to be older on average than the crucible steel Ulfberhts. Thus, they aren't counterfeit Ulfberhts. It's possible that groups 3 and 4, with a large range of variant spellings are counterfeits, but they would be counterfeits of group 2, not group 1.
Are the Ulfberhts really great swords? Some of them are certainly very good swords for the time, and quite respectable swords, from a functional/metallurgic perspective, even for much later times. But, considering the pattern-welded Ulfberhts, there were also many excellent pattern-welded non-Ulfberht swords, and also inferior non-Ulfberht swords. There are excellent swords in group 2, but these are not super-swords, not something unique to the Ulfberht "brand".
How do the group 1 swords (the "crucible steel" Ulfberhts) compare? Considering all of the steel-edged pattern-welded ones (groups 2 and 3), their edge hardnesses vary from about 200-500VPH (17-48HRC), with a few with edges of over 50HRC. The lower hardness ones are group 3, the harder ones are group 2 (these groups are separated on the basis of whether the blades were hardened). In comparison, the crucible steel ones are typically softer (200-300VPH (17-36HRC). A few are substantially harder (450-470VPH, about 45-46HRC), but these are still softer-edged than the hardest-edged pattern-welded Ulfberhts. On the basis of edge hardness, there doesn't seem to be any basis for claiming that the crucible steel Ulfberhts are better than the group 2 Ulfberhts. Edge hardness isn't the whole story, since ultra-high-carbon steels (such as crucible steels with carbon contents well over 1%, and other steels of such high carbon content) form carbide particles in the steel; even if the surround steel is soft, these carbides are very hard, and can result in good edge retention even on unhardened blades.
The high carbon contents of some of the group 1 swords can make heat treatment difficult. In particular, there is a relatively high risk of the blade being too brittle after quenching and tempering. One traditional solution to this problem was simply to not quench the blades - to air cool them instead. This results in blades that are quite soft, but also tough - soft and tough can be better than hard and brittle. As noted above, carbides could still give good edge retention. At least some of the crucible steel Ulfberhts were on the brittle side of things - of the 9 swords in Williams group I (the high-carbon end of my group 1), 4 had broken blades.
So, in summary, the group 1 Ulfberhts - the crucible steel Ulfberhts - don't appear to be notably better than the group 2 pattern-welded swords, and are somewhat inferior in terms of edge hardness and toughness. Even if the group 2 swords weren't older, they still wouldn't be inferior counterfeits.
Are the crucible steel Ulfberhts actually made from crucible steel? We don't know. The low slag content, and the very high carbon contents of many of the swords, certainly suggest it as a possibility. The trade connectedness of the Baltic region with Central Asia was strong at the time when these swords appeared, and Central Asia was exporting crucible steel at the time (these trade connections mean that Central Asian crucible steel is a better candidate than Indian crucible steel). The disappearance of such all-steel swords for a few centuries in the early 2nd millenium AD, after these trade links between the Baltic and Central Asia were disrupted further suggests that the steel was imported. Still, it isn't certain that the steel was imported; Kucypera (2014) demonstrates that such steels could have been made in Europe.
For Williams' analysis of Ulfberht swords, see Williams (2007) and Williams (2012). For more, see Stalsberg (2008).
References:
Kucypera, Paweł ; Hošek, Jiří,Hypereutectoid steel in early medieval sword production in Europe, Fasciculi Archaeologiae Historicae. Fasc. 27 (2014) http://rcin.org.pl/dlibra/docmetadata?id=54815
Anne Stalsberg, "Herstellung und Verbreitung der Vlfberht-Schwertklingen. Eine Neubewertung", Zeitschrift für Archäologie des Mittelalters 36, 2008, 89-118. English version: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.499.3126&rep=rep1&type=pdf
Williams, Alan. "Crucible steel in medieval swords." Metals and Mines. London (2007): 233-241.
Williams, Alan. Sword and the Crucible : A History of the Metallurgy of European Swords up to the 16th Century, BRILL, 2012.