I am trying to summarize and categorize here things.
There are general program such as GoodReader that are not good in small things such as searching or merging but good in reading with things such as light-adjustion. This is probably because the iPad's screen-area is limited, better to do a specific thing very well instead of many things poorly. I will list below more specific apps in iPad but many of them such as PDF Expert have iPhone version so iOS apps in that sense. Have a good reading!
I think if you want to do things very well in iPad you need to follow some sort of Unix-philosophy: less is more. Limitations such as area and virtual keyboard set clear design-guidelines such as avoiding extraneous things. New features always have trade-offs -- often in hard-to-measure things such as usability and accessibility. Despite lacking some objectiveness here I will outline apps in categories below. Please, feel free to suggest better categorization. You may find this thread here useful if you are new with iPad, iOS i or Apple ecosystem.
I. Apps prone in Reading
I. Papers app with things such as reference-lookup, grading and academic preview
II. GoodReader app with things such as Light-adjusting
III. Side-by-side app with cool intention but works badly, unfortunately no better alternative yet.
III. Apps prone in searching such as Content-search over all documents
I. PDF Expert
It has a content-search and indexation, may create downtime in copying DropBox things elsewhere -- a lot of small files apparently.
More about apps with content-search here.
IV. Apps with good support for formats such as mathematical formulae
iAnnotate is the only one currently able to read Windows proprietary formats well. Yes, I know: this is a bit painful particularly if you face this kind of files every now-and-then, you cannot yet find a killer app good in everything for iPad! For this kind of cases, iAnnotate helps you to see the math -formulae but you still need a desktop for editing or pay for Microsoft to edit the formats online.