So for the search results you could for instance discriminate between events and other posts by editing content.php and (in the default Twenty Twelve theme, around line 33) changing:
if ( is_search() ) :
To
if ( is_search() and ! tribe_is_event() ) :
And that would display the complete event description rather than the excerpt, but leave other non-event search results untouched. You could go further and pull in other bits of event data using functions like tribe_get_start_date(), too, but I’ll leave that to your imagination.
And now that I think of it, more importantly, is there a way to have the full post show within the category listing view?
For this one you would need to override list/single-event.php (please see our Themer’s Guide for details) and locate this line:
<?php the_excerpt() ?>
Changing it to:
<?php the_content() ?>
Hope that helps!