I have been using iPad 1 (64 GB) iOS 4.3.3 non-jailbroken, primarily as pdf reader for about six months now and had the same pdf problem with iBooks on iBooks version 1 and 2.
There is just one main reason (as far as i am concerned) to use iBooks as Pdf reader instead of some other free applications there, and that is Brightness control that seems to be able to really lower the Brightness and not faking it by just darkening the colors, what makes big difference if you read a lot at night or in the dark room like me.
I can transfer my pdf's to iBooks via USB cable though, although i don't use iTunes but 4Media iPad to pc transfer application (free version that lets you transfer one file at a time) and there was never problem as with Wi-Fi + dropbox, mail or any other application that would just not show that "open in iBooks" while dozen of other applications would have be there named.
As for eyestrain i never had problem reading on notebooks because i can lower Brightness and Contrast there as much as possible and read whole night and days, whereas iPad1 did hurt my eyes after a few hours of reading on the lowest Brightness level.
They say iPad 3 is much better in that regard also because it allows far lower lever of Brightness than iPad1 or 2, so i would probably get one sooner than later.
Now back to the topic !!! Thanks to the suggestion there about deleting superfluous pdf applications, i can now again see "open in iBooks" and open my pdf's in iBooks from Dropbox, Mail or other applications with sharing capabilities !!! as well as some other pdf readers like SideBooks that were also hidden so i had to transfer pdf's to them via cable also.
I've also, at first, turned iBooks off in the background but now i can open pdf's in ibooks even with iBooks icon there in the background so probably the main reason for success was deleting dozen of pdf readers and file transfering/organizing apps from iPad.
I still have about ten free pdf readers there because some feature nice curling page transitions like SideBooks, PerfectReader, Kobo etc. or some good highlighting and annonation or other capabilities.
I read pdf's in iBooks but do the highlighting/annotation in free apps like Adobe Reader because it is just click, double click or swipe away to get there. The same with some dictionary there in background while reading.
There is CHM+ Lite application (free version) that i usually use for WiFi transfers via my router ( http (with opera, firefox, chrome...) or ftp(with FileZilla client etc.)
Outside the room during the day i use eink reader though, Sony PRS T1, but usually cut off the borders of my pdf's before (if they are scans) and print them out in Adobe Acrobat or Viewer as 120x85 mm (landscape dimension of 6" readers) in Tile-all-pages-Mode, for the biggest possible letters and quickest page turning and handwriting/drawing on Sony's touchscreen.