The extent of which Anglo-Saxons were prominent in Britain is actually debated. They didn't keep great records and Gildas and Bede are quite unreliable.

They actually refer to Angles and Saxons as also meaning native Britons who were affiliated with the Germanic tribes that settled in the South East and that were later relegated to the East (at that point possibly meaning more native Britons).

"Heinrich Härke states:

It is now widely accepted that the Anglo-Saxons were not just transplanted Germanic invaders and settlers from the Continent, but the outcome of insular interactions and changes."

Anglo-Saxons are now thought to have come over relatively peacefully and while there was occasional conflict, the native Britons actually imposed taxes on the migrants after the battle of Badon (I believe it was then).

We have also found Anglo-Saxon burials that DNA evidence shows that the men buried there were native British and the women surrounding them were Scandinavian, indicating a level of intermarriage that wouldn't come from invasion.

A study by Researchers from the University of Durham and the British Geological Survey in 2004 found that of 24 Anglo-Saxon burials, only 4 of the buried men seemed to have come from outside of Britain.

Simply put, there is no archaeological or unbiased historical sources to suggest that Angles and Saxons invaded Britain and displaced natives.

Instead, it appears that there was gradual assimilation of a small amount of continental settlers and occasional conflict.

During the AS migration period there was also migrations of Britons to other parts of Britain, including Gaels and simply migration between regions. This would also help explain "contemporary" historians views on mass migrations throughout the British Isles.

The Anglo Saxons connections to the Continent would of been invaluable, though. Trade would of prospered and this could of led to very valuable communities of immigrants, which would entice many natives to settle among them and for the two cultures to integrate.

Native Britons were thrown into a dark age where Roman infrastructure began to fail after the Empire dissolved and were constantly being raided by Scots, Gaels and Picts (who are also British).

One theory is that the native Britons asked for aid from Angles, Saxons, Jutes and Frisians (Germanic neighbours) in return for being allowed to settle in the South (later the East aswell) while Briton tribes reorganised themselves.

DNA evidence in British populations in the present day are also constantly changing in regards to the input of Germanic genetics and remains very shaky in regards to solid evidence.

So simply put, the idea of Britons = Anglo-Saxon (which is an idea that was very much reinvigorated during the Victorian age, where the idea of Anglo-Saxon Christians defeating Briton Heathens was appealing to the pious and Gildas and Bede, who were both early historians and Christians, also subscribed to this idea) is at best highly debatable.

But to answer the question of "Would Angles and Saxons look different?" chances are that they wouldn't. Angles and Saxons were both Germanic neighbours and are thought to share much DNA with various other Germanic and Scandinavian/Norse groups, too.

And in 1066 they would of spoken Old English with British regional dialects, I believe.

Follow-up question: did they fully understand each other or did they keep some of their own dialects?