Wow.
Forensic accounting. Interesting question. You suspect your client is cheating with digital forgeries!
Adding to Anand's reply above, one thing to note: you will see a modified date in the metadata (File / Properties / Description tab) not just because the content was edited (such as adding $10,000 to the bank balance), but also if any highlighting or comments were added to the file.
Example: in my bank statements, I add comments to them to flag major purchases or items that have been reconciled with our accounting system. My comments would trigger that the file was modified, yet no content had been edited.
Since the content of PDFs can be edited, it's difficult for a program to track what WAS there and what IS there now. I don't know of any tools that can track or identify where the content has changed, but if you knew someone with PDF coding experience, they might be able to spot some digital paper trails in the source code of the file itself. (Maybe one of our braniac PDF coders on this forum will chime in on this.)
If you could get ahold of the bank's original version (such as redownload a fresh copy of the PDF, or via warrant request PDFs from the bank itself), you could then use Acrobat Pro's Compare utility. Select both PDFs, click the button, and it compares the differences between the 2 documents, including formatting and edited content. But this works only if you have the original PDF.