First off, make sure your playing it on PC. Valve games were meant to be on the PC. Playing Half Life on a Console is kinda like playing Mario Brothers on a mouse and keyboard.
Secondly, you have to understand the initial appeal. The original Half Life came out over a Decade ago, where it pretty much set the new standard for FPS games. Being late to the video game hobby, it was probably my very first real video game personally. Besides the game itself (As well as its excellent expansions) it also brought us the polished engine that brought us some of the greatest mods ever, and an engine that is still being used by the mod community today. Say what you will about the kinds of people who play Counterstrike, it was a highly polished , very fun game that set down some incredibly deep roots. Just because most of the people still playing it today are nostalgia addicted psychopaths doesn't mean that there's not a lot to love.
Fast forward to 2004. Or from our perspective, travel back in time to 2004. 5 years. In video game years, this is like going from watching a present day movie to watching a silent movie. When HL2 first came out, the graphics had me awestruck. It was like watching a program on a computer in a science fiction film, except is was real. Somehow. Go back to the present, and realize that the Source Engine is still alive and well. How many computer related things from 5 years ago can still be sold as present day? Not a lot. Its not impressive anymore when compared to a lot of games, but it manages to hold its own, and stay in the same ballpark. It's like seeing a 98 year old man on the Olympic gymnastics team. Besides, certain features like the Physics, or facial animation, still blow most of the new-fangled technologies out of the water.
Next, there is the mods, and things that the user content community do. There's a lot of mods out there for Half Life, and many of them are very good. I'm no programmer, but I know that it would be hard to find a platform that's more user friendly then source. That earns a lot of loyalty from fans.
Now enjoyability is a subjective things. So I can only speak for me, and for those trends that most people seem to agree with me on. All the nitty gritty work that went into designing Half Life 2 is incredible. It might use the tools other shooters use, but it uses them better then any other shooter out there. The story is just right for this kind of game. Its present just enough to drive the character, and keep them wondering both in and out of game. It presents questions and hints of answers at a rate that constantly teases the player to want to know more, and they put the little touches in that make a huge difference in how you relate to the characters: Watch some of the developer commentary and you will see the surprising weight that can come from a simple gameplay mechanic, a throwaway line, a facial expression, etc. They include storytelling mechanics that are very iconic and memorable, and add real depth to the characters. (For example, if you say, "Talk like the G Man", everyone knows what that means). Gameplay is well paced, and filled with a wide variety of necessary skills which build on each other and continue to present new and different challenges. The shooting and mechanics are simple and intuitive enough, but they give all your actions and choices a real sense of individuality and uniqueness: For example, in many games all the guns might feel like there's a continuous stream of damage to varying degrees and accuracies, but in HL2 the Magnum feels very different from the Machine gun, which feels very different from the crossbow, which feels...well, you get the point.
Basically, Half Life may seem like its another shooter with graphics that are amazing only in a historical perspective. But real connoisseurs TEND (Not always, but tend) to greatly appreciate the hard work that goes into all the details. I suggest watching the commentary, and you might appreciate some things about it a little more.
Or maybe not. Just go with whatever you enjoy most. For a lot of people, that's HL2. I don't consider myself a fanboy per say, but I do personally have a great well of appreciation for the kinds of work Valve does. I don't think any other developers match it.