I will soon purchase an Xbox 360, and I was wondering about the differences between Ninja Gaiden and Ninja Gaiden Black, both of which are compatible with the 360.

Is Ninja Gaiden Black just an overall improved version of Ninja Gaiden. Should I just buy that? Or is it worth it to buy Ninja Gaiden with the Hurricane Packs? Or should I get both?

Get Black.

Black is basically the normal NG, but has all kinds of extras.

Get Black. No question there. More enemies, more difficulties, more weapons, more missions.

NGB is basically just an improved version of the game. The only slightly annoying thing is the last boss in black is much harder as they made him much more resitant to the best technique to kill him.

Here is the list from wikipedia of changes.
Changes from Ninja Gaiden
The following was changed from the original Ninja Gaiden:

Higher resolution textures are now used for Ryu
Changes to Story Mode
Composition of encounters varies with difficulty
Some items' location are moved on higher difficulties
Shop prices (item costs increase with game difficulty, and some weapon upgrade prices have been changed)
Scarab rewards varies with game difficulty (Dark Dragon Blade being a scarab reward for higher difficulties being one of the changes)
Bosses now have minions accompanying them on higher difficulties
Clearing respawns of encounters no longer scores points
Enemy specifications have been tweaked (e.g. increased aggressiveness, new guard breaking and grab attacks, more frequent blocking of Flying Swallow, base essence)
A few foes (nightmares, Awakened Alma) are more resistant to the Unlabored Flawlessness' damage
The camera can now be manually rotated
The weapon Kitetsu no longer drains Ryu's health, and is upgradeable
Guillotine Throw command has been changed
Ryu is now able to charge up Ultimate Techniques without needing essences; successful Ultimate Techniques also score 2000 / 5000 points

Additional Features
The following are new additions, not found in the original Ninja Gaiden:

Ninja Dog (only for Story Mode) and Master Ninja difficulties
New encounters, and additional starting weapons for higher difficulties of Story Mode
A few additional save points, and several new in-game cutscenes in Story Mode
Mission Mode, four new costumes, and the Ninja Gaiden arcade game as unlockable features
New weapons and items
The Lunar and Smoke Bombs
Restoration items (Ayane's Ration, Ayane's Ration Bundle, Fragrance of Dayflower, Fragrance of Hydrangea)
Ribbons (function exactly like Armlets; only in Story Mode Ninja Dog difficulty)
Jewel of the Smith, which can upgrade weapons (only in one of the Mission Mode missions)
New foes
Explosive bats, silver samurais, super MSATs, and super soldiers
Ninjas of wisdom (purple clad ninjas who can throw Windmill Shurikens), and flame ninjas (red clad ninjas whose blows inflict additional fire damage)
Dino fiends (club wielding giants wearing triceratops skull masks), and cat fiends (black, and blue versions)
Crow shadows (commonly known as armored imps, or sliders)
Nightmare fiends (commonly known as Vigoorian Berserkers)
Black sargeras (commonly known as armored moat fishes)
New bosses
Doppelganger fiend, Nicchae, and Ishtaros

Removed Features
The following were removed from the game, compared to the original Ninja Gaiden:

The Armlet of Tranquility (from Story Mode, but available in certain Mission Mode missions)
The future ninja costume, and the three ported SNES Ninja Gaiden Trilogy games unlocked as bonuses in Story Mode
Successive Play

Black a more complete version.

i'm gona buy this game soon

There is no debate at all, Black has everything the normal version did plus more, it also has the Ninja Dog mode if you can't handle the game :)

Sigma, just kidding, Black. It has everything the first one does and more, including a much better camera.

Okay, so it's unanimous. I was going to buy Black without question but then I saw there were some things that were removed (The future ninja costume, three ported SNES Ninja Gaiden Trilogy games, Successive Play) and I started wondering whether these things were important. I can see that they are not, at least not that much. So I will buy Black. I got the 360 yesterday, by the way.