I can only speak for Wessex, but it's probably an unexciting mixture of both. Germanic mercenaries were used to augment local militias, so there is an element of assimilation from the Roman period, but the Saxons also attacked the southern coast from about 365 onwards to the 5th century, where we first start to see Saxon settlements. Cunliffe suggests that groups were allowed to settle, to provide a buffer against future invaders (a Roman technique). They continued to probe Wessex, fighting a number of battles which the indigenous Britons repulsed. It's difficult to assess the levels of atrocities committed, firstly because our literary sources for the period are weak and contested, and secondly the burial remains are somewhat haphazard for this period, but there are the skeletons of about 5 people and about a dozen cattle thrown down a well at Brislington, and another 3 bodies in a well at North Wraxall, but both are difficult to date with certainty to this period. Because the Roman empire collapsed, it meant that the trade routes gradually collapsed and the amount of goods and money became scarce. Grave goods are very poor for this period (as compared to the previous millennium and to the much more interesting Anglo-Saxon period from the 5th century), and it's hard to tell whether something in a grave comes from the period or earlier - is it grandma's valuable vase, passed down for 3 generations or something that comes from your generation.

Depending on how you want to define Anglo-Saxon, Cerdic and Cynric did attack the Isle of Wight (a Jute possession), and southern Hampshire in general (more Jutish territory) and continued to wage wars on the Britons at Barbury and possibly the Jutes at Portsmouth if Bede is to believed. The Wiki map of Jutish territory is probably good enough.

We bedeviled by the problems of dating material goods with any precision, and that makes identification of specific groups somewhat difficult.