I'm an avid fan of science fiction. A fan of most kinds of science fiction, in fact. From soft to hard, from dark to light, and from pop to speculative. As a result, I'm a fan of both the Half-Life and Halo series.
However, I'm a bigger fan of darker, hard-and-soft-sci-fi styles of story telling. I prefer Star Trek to Star Wars, for example. As a result, there is just so much more for me in the Half-Life series.
A better story filled with a host of hard-and-soft-sci-fi concepts and contemplations. A more interesting and diverse cast of characters and locales. Believable concepts, events, and aesthetics intermixed with a vast array of otherworldly creations. A higher degree of depth to the narrative. Foes that feel more dangerous and threatening. Story elements that delve into technological, scientific, and socio-political ponderings.
All around, the Half-Life series has always offered me a more immersive and more compelling narrative experience than the Halo series has.
Now, in terms of gameplay they're hard to compare. They offer different experiences, all things considered. Experiences, I might add, that I enjoy equally. However, I think I find the level designs, sound design, and general aesthetics of the Half-Life series a bit more inline with my tastes.
In the end, I love both series. I've had countless hours of entertainment with both. Even to this day I still occasionally dive into both series to immerse myself in their lore. It's just that the Half-Life series gives me more of what I want.