Here are the specialization bonuses according to class:
1st Fighter Specialization: +1 STR, ability of having 4 proficiency points in a weapon
1st Mage Specialization: +1 INT
1st Thief Specialization: +1 DEX
2nd Fighter Specialization: +1 STR, +1 CON, +3 MAXHP, ability of having 5 proficiency points in a weapon
2nd Mage Specialization: +2 INT, +1 WIS, +5 Lore
2nd Thief Specialization: +2 DEX, +1 Luck
Note: Specializing in two different classes will give the Nameless One the first level specialization for both classes.
Note 2: Specializing in a particular class also unlocks particular tattoos in Fell's Studio.
- The Nameless One, Annah and Dak'kon can use Tattoo of the Warrior and Tattoo of the Supreme Warrior (cumulatively for one strong character

- Only Annah and the Nameless One can use the Tattoo of the Thief or the Tattoo of the Master Thief (wear them cumulatively, and you won't have to pay for most purchases

- Only Dak'kon and the Nameless One can use the Tattoo of the Art or the Tattoo of the Magi (Dak'kon could kick Ignus' behind wearing these together

Analysis:
From the statistics alone it seems that double specializing in a single class gives better bonuses than single specialization in two classes. (+3 to +4 cumulative character point increases with bonus attributes as opposed to +2 cumulative character points for single specializations.)
While double specializing as a Mage gives the best attribute increase (+4 cumulative character point increase as opposed to +3), the +5 Lore is almost useless especially with the many Charms of Infinite Recall floating about in the realms. Double specializing as a Mage does ensure that you will always be able to activate the Wish Scroll when the time comes. Of course, the Wish Scroll does not really require a specialized mage, just a level 12+ mage.
(Double specialization as a mage also gives (lightly) more experience points from the Ravel encounter)
Double Specializing as a Thief gives the unique +1 Luck which can be combined with luck enhancing items such as the Tattoo of the Master Thief, Tattoo of the Redeemer and Punchdaggers of Moorin for some pretty impressive effects. Furthermore, only the Wish Scroll and Xariach's Heart gives permanent bonus DEX increases, as opposed to the numerous ways to increase your INT and WIS along the way.
Double Specializing as a Fighter gives the unique 5 proficiency points in a chosen weapon, which is active even when using other classes. Furthermore, if the STR bonuses are taken when charater STR=18, the +1 STR bonus to STR=19 is equivalent to 6 character points, since the normal STR progression when taken at level is:
18
18/30 - 1 character point
18/60 - 2 character points
18/90 - 3 character points
18/99 - 4 character points
18/100 -5 character points
19 - 6 character points
This also works for single Fighter Specializations, making Single Specialized fighters comparable to double specialized characters (though just barely).
Of course if the Nameless One is Lawful and has STR=18 when the party reaches Curst, the specialized Fighter bonus STR advantage becomes moot since Vhailor gives the STR boost to Lawful characters.

So that all said, what is your favourite way to specialize the Nameless One?