Byte ordering for multibyte characters in SQL Server versus Oracle
What you are seeing is Little-Endian encoding that SQL Server uses to store Unicode characters (more precisely, it uses UCS-2 LE).

More on Little-Endian here: Difference between Big Endian and little Endian Byte order


I don't know how it was possible that 


  When I use DUMP in Oracle or convert to VARBINARY in SQL Server the
  data matches exactly except for the bytes for this character


All the Unicode characters stored in SQL Server, converted to binary, are "inverted", I mean, to see the real codes you should divide them in groups of 2 bytes and invert the order within every pair.

Example:

declare @str varchar(3) = 'abc';
declare @str_n nvarchar(3) = N'abc';

select cast(@str as varbinary(3));
select cast(@str_n as varbinary(6));


The result is 

0x616263

0x610062006300


As you see in case of Unicode characters bytes are inverted:
"a" is represented as 0x6100 and not as 0x0061.

The same story is about 0x25E6 that is real Unicode code while in binary representation in SQL Server you see it as 0xE625, i.e. inverted.