Are you interested in a comparison of "styles" only or also themes?
Stylistically, Irving wrote more in the style of the century previous to
his own (and hid his deeper purposes by cloaking them in the veil of
legend and fantasy), while Twain preferred the Realist style of
his own time, although he also demonstrated a willingness
to work in the realm of the fantasicic. Thematically, they are much
closer, for both were addressing issues of their times.  In
particular they both addressed the effects of technological progress on
the structure of society.

I just gave a paper on Irving, and (obviously, since I'm on this list)
also study Twain, so if you'd care to continue privately, please feel
free to post me directly.

Jeri Zulli
George Washington University