I normally use point sizes, but I have also been known to dabble with pixel sizes.
In brief, points are a standard method of setting type size in print: if you expect your site visitors to regularly print copies of your webpages with type sizes set in points it may be more legible in print. The obvious variable here is your visitors printer preferences and web browser preferences in relation to printing.
Now, since point sizes are not directly equal to the pixel matrix used by your monitor there is a certain amount of 'approximation' involved in displaying them. This can cause your fonts to be less legible.
Older web browser (IE 5 and under) have difficulty from scaling text when the fonts are set in point sizes.
All newer browser software on PC and Mac platforms has long since addressed the issue but as in all things, some browsers cope better than others and a good testing program for your web will pick up and highlight any issues.
I almost always use points and have done for some time now. The argument in favour of pixel sizing fonts is not very compelling these days when even low quality domestic printers coupled with predominantly high version browser software can produce good output in print, while IE as the majority market share browser can normally cope with most things that come its way without mangling your pages too much.
Points for me, but pixels if you want to prevent browser software from altering your pages on the fly.
Sorry if this raises more questions than it answers.