A nice illustration here of how body size is a distinguishing feature in separating Crossbill types (scroll down a bit, and warning, there are images of dead crossbills):
Notice how the the juv female Parrot, as it is sitting (alive) on the fence wire, does not have an apparently massive bill. Yet in the hand it is considerably larger than Common Crossbills. It does show the sometimes evident "small eye" syndrome though ! In the field it is often difficult to judge overall body size unless you have the luxury of a mixed group, though Commons to me are similar in size to Greenfinch (or just bigger than Chaffinch, which are often nearby). Parrots by comparison are just a bit smaller than a Starling or (smallish) Waxwing (eg. about 50-55g). Bill structure can seem to be in proportion to body size in many specimens thus some Parrots could potentially be confused with larger billed Commons without calls and without a strong idea of body size (indeed they were on Bird Forum a few years ago, though many of the birds had wide bills with strongly decurved culmens as well as "strong" necks.