While the main poppler developers, who IIRC are three guys from Spain, have made a heroic effort, poppler is really not that good. Poppler was created by ripping out code from Xpdf and making it into a library.
If you look at the code, it is not really well architected. Here is a file I found a problem in - http://cgit.freedesktop.org/poppler/poppler/tree/poppler/Tex... . Take a look at that file and judge for yourself if it follows "Code Complete" type suggestions.
One reason I looked in that file is poppler does not deal well at all with many map PDFs like http://web.mta.info/nyct/maps/busqns.pdf or some others I have on my hard drive. They take forever to load.
Some PDFs have caused the applications using poppler to crash, although some of those have been patched. It's not as bad as it used to be, but still. My patch to speed up the bus map PDFs was not accepted. Then there are features like being able to enter data into PDFs and such. Compare and contrast Adobe's official Acrobat app for Linux and a PDF reader based on poppler like evince.
So the answer is a standard one - code architecture, bugs and features. The answer would be to take the PDFs that Adobe Acrobat handles but which poppler doesn't in terms of bugs and features, and see how pdfium handles them.
Of course, it's possible pdfium will handle those but fail on an entirely different class of PDFs and their pdfium specific bugs.
The PDF standard is a fairly large one. What features does pdfium handle which poppler doesn't? What percentages of PDFs crash the viewing application, or don't render correctly compared to poppler? And so forth.
I should also add that poppler usually depends on cairo for vector graphics. So once in a while the fail for a pdf is on cairo, not poppler. I have seen some of those fixed, some not.
I compared the speed (plain text extraction) of xpdf, poppler and mupdf on 100k PDFs. mupdf is in 95% cases the fastest, then comes xpdf and then poppler (the latter two crashed on a few files). SumatraPDF viewer went from poppler-only to two engines (poppler & mupdf) to mupdf+patches. At the moment from my experience SumatraPDF has the fastest and most reliable PDF engine, that is open source. So it will be interesting how this Chrome PDF open source engine (based on Foxit?) performs outside of Chrome as standalone library/commandline tool.
