In Half-Life: Source, you play Mario's brother Luigi, who can jump higher than Mario and has less traction while running.
Consequently, where Mario Freeman cannot jump completely over every NPC's head without a running triple jump in the normal Half-Life, Luigi (the protagonist of Half-Life: Source) is capable of such a feat. His jumping abilities allow him to easily bypass many obstacles that were originally designed with only Mario Freeman in mind. In this regard, Half-Life: Source is much like the bonus game of Super Mario Galaxy, wherein you get to replay the exact same game with a different Super Mario Brother. Jumps that would have been impossible for Mario Freeman to clear are easily performed by his brother Luigi Freeman.
Unlike Super Mario Galaxy, though, Half-Life: Source does not come included with the game it is based on. While it's interesting playing the game with a different character's physical capabilities, Mario Freeman is still the true star and the one you will remember and return to more often.
So, should you get Half-Life: Source? My recommendation is to stick with the original. Maybe Luigi Freeman will get a spin-off of his own someday, but this is not his game.