you'd need to do it with JavaScript.
but bear in mind that the browse could change width - if for example you went to the "next" page, and it decided it needed more space.
This is out my head, so you may need to adjust a bit;
p_web.script('$("#displayid").width($("#browseid").width());')
where displayid, and browseid are the id's of the respective fields. (The browse has a div around it with the correct size.) You will need to use Firebug to see what the names are. Also, remember, it is case sensitive.
You can embed the above line in one of the "value" routines - I'd probably add it to the Display, or Browse, Value routine.
Cheers
Bruce