What is the difference between using hook_views_pre_render() or preprocess functions? What is the difference in using hook_views_pre_render(&amp;$view) instead of using 
[THEME_NAME]_preprocess_views_view_table_[VIEW_NAME] . I am just changing the '#markup' of field.
hook_views_pre_render() is being used in custom module and 
[THEME_NAME]_preprocess_views_view_table_[VIEW_NAME] is used in template.php file ?
Behind the scenes they're pretty different (one is a hook provided by Views, the other part of the theme system). Practically speaking, as a module/theme developer you'll see very little difference. What you can do in one you can do in the other, and hook_views_pre_render() can even be implemented in a theme.

I'd say just pick the one which offers you the most intuitive/simple way to make the changes you need to. If the theme preprocess requires more complex logic/code use the pre_render hook, and vice versa.