Sorry for very late response, and note that I'm not so specially well familiar with the details in Anglo-Saxon clothing.

Unfortunately, we have several reservations (limitations) to reconstruct the trends of the female clothing in these two eras and areas (Anglo-Saxon England and Viking Age Scandinavia? or somewhere like Danelaw England?):

• We don't have much sources especially for non-noble females in respective ages, so it is not so unlikely that the archaeologists have to rely on reconstructing the clothing based on rather similar and meager sources.
• 'Anglo-Saxon period' in the British Isles lasted much longer, from ca. 5th century to the 11th century, than 'Viking Age' in Scandinavia (from ca. 800 to ca. 1050), and some regional variations of the material culture in clothing customs within the Anglo-Saxon dominated areas could have been discerned since quite an early period. Thus, it also means that the answer can be varied depending on the comparison between which period/ areas of Anglo-Saxon female clothing and that of Viking age women.

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Anyway, it is true that Anglo-Saxon high social rank women in the 6th and early 7th century wore similar style of clothing with Scandinavian women in the 9th and early 10th century, at least at a first glance.

Both seem to put dress-style clothing, sometimes called peplos, often held by two brooches sometimes on both sides of her shoulder. The fabric materials of their respective clothing were also similar: home made wool and flax linen spun were their favorite materials, and the weaving technology used in clothing of 6th and 7th century Anglo-Saxon women is said to have have derived from the 5th and 6th century Denmark and Northern Germany. In other words, females around the North Sea in the 6th and 7th century could put more or less similar clothing on.

We should be careful of identifying the background of this shared material culture as a result of large-scale 'migration of the Anglo-Saxons' into SE British Isles, however. Recent correlation between archaeological evidences as well as scientific researches reveal that it was the local population of Great Britain, rather than new comers out of the Isle, actively adopted the new accessory of 'Anglo-Saxon' style in the 5th century (Oosthuizen 2019: 74-75).

On the other hand, Anglo-Saxons in the 8th century Britain developed some new styles of clothing (at least for men), thus diverging a bit from their shared 'North Sea' material culture.

Another, more important difference between these two can be found in the brooches holding the garment up on the shoulder: While Anglo-Saxon women in the 7th century used various shapes of brooches, like this square-shape head one, women in the Vikings Ages tend to prefer to wear the oval shape brooches.

Researchers of the Viking Age now suppose that this kind of oval shape brooches played an important role in gendered cultural identity of Norse-Scandinavian women dispersed across North-Western Eurasia in the Viking Age (Jesch 2015: 94-97). It means that few Viking Age women would mistake the female clad in Anglo-Saxon style dress with the square shape brooches as one of their own sort, since the style of these tiny brooches really matters.

Some experts also might be able to identify some more subtle difference of materials: To give an example, cattle leather got more extensively employed for the clothing of Norse (Viking) settlers, and more dense woven wool, called vaðmal, originated in Western part of Scandinavia as well as their settlements in the North Atlantic, also came to the British Isles in the late 9th and early 10th century, together with such settlers (Carver 2019: 119).

References:

• Carver, Martin. Formative Britain: An Archaeology of Britain, Fifth to Eleventh Century AD. London: Routledge, 2019.
• Jesch, Judith. The Viking Diaspora. London: Routledge, 2015.
• Oosthuizen, Susan. The Emergence of the English. Kalamazoo, MI: ARC Humanities, 2019.