Compare and contrast the acquistion of Texas and the Southwest with that of Oregon.

There are more differences between these two acquisitions
than there are similarities.

The only real similarity
between these two is that both places were, originally, taken by Europeans from the
Native Americans.  In both places, there were still Native Americans that had to be
"removed" or "pacified" after the US acquired the new
territory.

There is a significant difference in how the US
acquired each area, though.  The US acquired Texas and the Southwest through coercion. 
Mexico did not recognize Texas's independence when the US annexed Texas and it took the
Mexican-American War to get the rest of the Southwest for the US.  By contrast, the US
got the Oregon Territory peacefully.  The US got Oregon by making a treaty with Great
Britain.  There was no coercion involved.

So, the
similarity is that both areas were originally taken by force from Native Americans. 
However, the US took the Southwest by force from Mexico but got Oregon peacefully from
Great Britain.