Better to view it on a wide screen.

It's all about cyrillic characters:
¨¸ comparing to Åå and
Éé comparing to Èè

characters (first code is cp1251):
å 0xE5 = U+0435 : CYRILLIC SMALL LETTER IE
Å 0xC5 = U+0415 : CYRILLIC CAPITAL LETTER IE
¸ 0xB8 = U+0451 : CYRILLIC SMALL LETTER IO
¨ 0xA8 = U+0401 : CYRILLIC CAPITAL LETTER IO
è 0xE8 = U+0438 : CYRILLIC SMALL LETTER I
È 0xC8 = U+0418 : CYRILLIC CAPITAL LETTER I
é 0xE9 = U+0439 : CYRILLIC SMALL LETTER SHORT I
É 0xC9 = U+0419 : CYRILLIC CAPITAL LETTER SHORT I 

from http://www.unicode.org/Public/MAPPINGS/VENDORS/MICSFT/WINDOWS/CP1251.TXT

I compare several collations in cp1251 and utf8 character sets.
SQL SELECT looks like (cp1251 hex codes):
select '¸' = '¨', 'é' = 'É', 'z' = 'Z', 'å' = '¸', 'è' = 'é', 'È' = 'É', 'å' >= '¸', 'Å' = '¨', 'è' > 'é', '¨' > '¸', 'É' > 'é', 'Á' > 'á', 'L' > 'l';
        B8    A8   E9    C9   7A    5A   E5    B8   E8    E9   C8    C9   E5     B8   C5    A8   E8    E9   A8    B8   C9    E9   C1    E1   4C    6C

Compare case sensitive collations
---------------------------------

mysql> set names cp1251 collate cp1251_general_cs;
mysql> select '¸' = '¨', 'é' = 'É', 'z' = 'Z', 'å' = '¸', 'è' = 'é', 'È' = 'É', 'å' >= '¸', 'Å' = '¨', 'è' > 'é', '¨' > '¸', 'É' > 'é', 'Á' > 'á', 'L' > 'l';
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
| '¸' = '¨' | 'é' = 'É' | 'z' = 'Z' | 'å' = '¸' | 'è' = 'é' | 'È' = 'É' | 'å' >= '¸' | 'Å' = '¨' | 'è' > 'é' | '¨' > '¸' | 'É' > 'é' | 'Á' > 'á' | 'L' > 'l' |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
|         0 |         0 |         0 |         0 |         0 |         0 |          0 |         0 |         0 |         0 |         0 |         0 |         0 |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
Correct

mysql> set names utf8 collate utf8_bin;
mysql> select '¸' = '¨', 'é' = 'É', 'z' = 'Z', 'å' = '¸', 'è' = 'é', 'È' = 'É', 'å' >= '¸', 'Å' = '¨', 'è' > 'é', '¨' > '¸', 'É' > 'é', 'Á' > 'á', 'L' > 'l';
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
| '¸' = '¨' | 'é' = 'É' | 'z' = 'Z' | 'å' = '¸' | 'è' = 'é' | 'È' = 'É' | 'å' >= '¸' | 'Å' = '¨' | 'è' > 'é' | '¨' > '¸' | 'É' > 'é' | 'Á' > 'á' | 'L' > 'l' |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
|         0 |         0 |         0 |         0 |         0 |         0 |          1 |         0 |         0 |         0 |         0 |         0 |         0 |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
Wrong!

The 1 (true value) in second result is a error! It has to be 0 (false) (sorting issue)


Compare case insensitive collations
-----------------------------------

mysql> set names cp1251 collate cp1251_general_ci;
mysql> select '¸' = '¨', 'é' = 'É', 'z' = 'Z', 'å' = '¸', 'è' = 'é', 'È' = 'É', 'å' >= '¸', 'Å' = '¨', 'è' > 'é', '¨' > '¸', 'É' > 'é', 'Á' > 'á', 'L' > 'l';
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
| '¸' = '¨' | 'é' = 'É' | 'z' = 'Z' | 'å' = '¸' | 'è' = 'é' | 'È' = 'É' | 'å' >= '¸' | 'Å' = '¨' | 'è' > 'é' | '¨' > '¸' | 'É' > 'é' | 'Á' > 'á' | 'L' > 'l' |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
|         1 |         1 |         1 |         0 |         0 |         0 |          0 |         0 |         0 |         0 |         0 |         0 |         0 |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
Correct

mysql> set names utf8 collate utf8_general_ci;
mysql> select '¸' = '¨', 'é' = 'É', 'z' = 'Z', 'å' = '¸', 'è' = 'é', 'È' = 'É', 'å' >= '¸', 'Å' = '¨', 'è' > 'é', '¨' > '¸', 'É' > 'é', 'Á' > 'á', 'L' > 'l';
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
| '¸' = '¨' | 'é' = 'É' | 'z' = 'Z' | 'å' = '¸' | 'è' = 'é' | 'È' = 'É' | 'å' >= '¸' | 'Å' = '¨' | 'è' > 'é' | '¨' > '¸' | 'É' > 'é' | 'Á' > 'á' | 'L' > 'l' |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
|         0 |         0 |         1 |         0 |         0 |         0 |          1 |         0 |         0 |         0 |         0 |         0 |         0 |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
Wrong in columns (starting from 1): 1, 2, 7. First 3 columns have to be 1 and the rest - 0

mysql> set names utf8 collate utf8_unicode_ci;
mysql> select '¸' = '¨', 'é' = 'É', 'z' = 'Z', 'å' = '¸', 'è' = 'é', 'È' = 'É', 'å' >= '¸', 'Å' = '¨', 'è' > 'é', '¨' > '¸', 'É' > 'é', 'Á' > 'á', 'L' > 'l';
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
| '¸' = '¨' | 'é' = 'É' | 'z' = 'Z' | 'å' = '¸' | 'è' = 'é' | 'È' = 'É' | 'å' >= '¸' | 'Å' = '¨' | 'è' > 'é' | '¨' > '¸' | 'É' > 'é' | 'Á' > 'á' | 'L' > 'l' |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
|         1 |         1 |         1 |         1 |         1 |         1 |          1 |         1 |         0 |         0 |         0 |         0 |         0 |
+-----------+-----------+-----------+-----------+-----------+-----------+------------+-----------+-----------+-----------+-----------+-----------+-----------+
Wrong in columns (starting from 1): 4, 5, 6, 7, 8. First 3 columns have to be 1 and the rest - 0