There are a number of major influences on how a person is perceived. Two significant ones are the face at rest and the speaking voice. Jeffrey Hunter has a naturally serious voice, at a deeper timber than Shatner. Also, his face tends to have a more stern look about it, mostly due to his eyebrows and deeper set eyes, whereas Shatner's face has a more rounded and softer appearance. By this alone, it automatically casts a different feel about the two actors.
Christopher is right, that we do have the unfortunate handicap of only one Star Trek episode with which to assess Hunter.
Here's a photo montage I whipped up in black & white, showing Hunter and Shatner. Now, believe it or not, it's hard to find photos of Shatner smiling in black & white, but very easy to do so with Hunter! This works against the point I was trying to make. But even here, you can see how Shatner's face is softer compared to Hunter, even without smiling much.