SourceMod is server modification for any game that runs on the Half-Life 2 engine. It is a powerful, highly optimized platform for scripting plugins and handling server administration. The default package comes with a base set of plugins, but there are over 450 plugins in the community.

Basic Features (Users)
An easy to use, deeply fine-grained permissions system (SQL compatible)
A highly configurable admin menu
Reserved slots
Flexible map management plugins (nominations, rock the vote, etc)
Basic commands such as kicking/banning/slapping/muting players, changing cvars, etc
Various voting commands
Chat spam protection
Comprehensive chat triggers for both users and administrators
Easily translatable
SourceMod is highly optimized and ideal for getting the most performance out of your Source servers, without the complexity of writing C++ code.

Scripting Features (Developers)
Administration - Comprehensive API for developing administration systems.
Clients - Working with in-game client information and callbacks.
Commands - Creation, hooking, and overriding of client and server console commands.
ConVars - Creation, hooking, and retrieval of console variables.
Database - Abstracted database access.
Engine - Access to many Half-Life 2 engine features, with more constantly being added.
Entities - Changing and retrieving entity properties, both named and numbered.
Events - Creating, firing, and hooking of Half-Life 2 GameEvents.
Files - Access to the filesystem.
IPC - Advanced inter-plugin communication, similar to AMX Mod X.
Menus - Abstracted menu API for creating uniform menus across mods
Messages - Sending and hooking UserMessages.
Parsing - Advanced, highly optimized text parsing.
Timers - Creation of timed events.
Translation - Multi-Lingual phrase file lookup.

What makes SourceMod different? (Developers)
Speed - SourceMod is lightning fast, and this is not an idle boast. Every plugin is loaded into memory and converted to raw CPU code. Great care is taken to make sure every hot area in SourceMod is as fast as it should be. The scripting language is statically typed and does not require garbage collection.
API - The majority of work in SourceMod occurs in making the API the best we can. When adding any interface or function, we ask the following questions:
Does it represent an optimized solution?
Would anyone use it?
How confusing is it?
Does it match the most probable common usage?
Will it be possible to extend it in the future?
Does its name represent what it does?
Does its name conform to other similar functions?
Extensibility - SourceMod is completely extensible. SourceMod provides a complete C++ API for extending both SourceMod and the Plugin event/native API. You can also write C++ plugins.
Open-Source - SourceMod, its extensions, and its plugins, are all open source under the GNU General Public License!

Reference(s):
http://www.sourcemod.net/about.php

Image(s):
http://media.steampowered.com/steamcommunity/public/images/avatars/e8/e8fb2963350dff03db5f70633174a19f3d43655d_full.jpg

AMX Mod X is a versatile Half-Life metamod plugin which is targetted toward server administration.
It has a wide array of scripting capabilities so people can write "plugins", or files which add on to a mod's functionality.
Plugins can take form in administrative services (adding new admin commands), statistics generation (StatsX), fun additions (godmode, etc), gameplay changes (WC3, CSDM), and much, much more!
You can also write modules to expand the functionality of AMX Mod X and add to the scripting language.

AMX Mod X and AMX Mod
AMX Mod X was originally based on AMX Mod, a similar Half-Life modification by OLO. However, AMX Mod began to slip into poor project policies (lack of public input, no open source enforcement, no central source code maintained, and much more).
Due to the dead appearance of the project as all maintainers had disappeared into oblivion, the AMX Mod X project was started.
Since then, the AMX Mod X project has come a long way. Nearly every portion of AMX Mod has been either rewritten from the ground up, cleaned up, or changed to work in a new system.
AMX Mod X is not AMX Mod. And better yet, it's almost fully backward compatible.

Reference(s):
http://www.amxmodx.org/about.php

Image(s):
http://www.amxmodx.org/images/amxxlarge.jpg