currently 1080p (1920x1080) is the most common monitor and television format. i believe there is a slight difference in pixel arrangements between the two but in general they are similar.
some smaller tvs are only 720p so any step up to 1080 would be an improvement.
a 2560x1440 or 2560x1600 would be a slight step up in sharpness (like 7%) but can cost 300% more then a 1080p screen making it not very good in price vs performance. what you do gain instead of sharpness is a larger screen while keeping the ppi of smaller monitors.
what upgrade route you go depends upon your useage.
you could go with a 2560x monitor, 1080p monitor or large 1080p television depending on why you feel you need to upgrade and what you want to use the monitor for.
i myself use a 40" 1080p television as a screen. it suits frequent movie watching, gaming and only occasional msoffice/general tasks well.