This is a question that has become somewhat of a trope in early English history, as well as women's studies. Pauline Stafford in "Women and the Norman Conquest" points out that the history of this idea is itself an interesting historical question which points to the intentions of the various writers who proposed it. From Tacitus in 1st century Rome to John Mitchell Kemble in 19th century London, various writers have pushed the idea that the Germanic/Anglo-Saxon woman was better-off than women of other cultures.

Unfortunately, they all had rather interesting reasons for propounding this view:

"Tacitus' Germanic women, for example, were a foil to the decadence of contemporary Rome, which he, like many of his contemporaries, blamed on women. Society for him is healthy when women are chaste, mothers and controlled by their husbands, not when they visit the theatre and the baths, exchange love letters with their lovers and fail to breastfeed. Tacitus constructs a Germanic woman with which to beat the Romans of his own day"

[...]

"Kemble, using Anglo-Saxon women against the feminists of his own day, was happy to echo the ancient Roman. He placed Anglo-Saxon women and their high status firmly within the home, that sacred place where women were 'near akin to divinity'. But there they should stay.[...] Early English women happily accepted men's representation of them in public life, content to be beings of a higher nature. They did not clamour and rave for the rights of women. Kemble's Teutonic women are a mid-nineteenth-century conservative male pipe dream."

Stafford does a pretty good job dismantling the view that the Norman Conquest ended a sort-of Golden Age for women in England. She points out that, while many have claimed that Anglo-Saxon women were, ostensibly, given greater legal rights with regards to holding, inheriting and divesting property, pre-Conquest women only held about 5% of the land, and most of that was held by only 8 women who were from particularly powerful noble families or the Royal Family itself. Her handling of the morning gift/dowry idea - that Anglo-Saxon women had control over land that they brought into the marriage, while Norman women did not - is also excellent. She shows that, not only did dowry exist in pre-Conquest England but that examples exist of post-Conquest women controlling both dower and dowry.

In the end, she concludes, "there are many [serious arguments] for abandoning the idea of 1066 as a turning point of great significance in the history of English women, and for jettisoning the Anglo-Saxon Golden Age. Both ideas are more a product of the political concerns of past historians than of the experience of the eleventh century"

In the area of monastic government women had some more rights than they did after the Norman Invasion. Anglo-Saxon Britain is one of the few places in which it wasn't terribly unusual for women to rule over religious communities (in the style of Frankish double houses) of men and women. Hilda of Whitby is the classic example. She even presided over the Synod of Whitby which brought Celtic and Anglo-Saxon Christianity closer in line with Mediterranean Christianity. Indeed thanks to Celtic influence, in at least Northumbria leaders of religious communities had more political sway than bishops in some cases.

However, the Normal Conquest was not the reason for this practice coming to an end. During the sweeping monastic reforms of the 6th and 7th centuries, the Benedictine rule gradually came to replace Celtic, Frankish, and local rules throughout all of Europe, including Britain. And under Benedictine rule, the structure of the double house was not permitted. By the time the Normans came on to the scene, women presiding over religious communities of men and women were relics of a bygone age.

Source: The Emergence of Monasticism by Marilyn Dunn