In brief, each School of Thought has its own collection of hadith books, and also its own methodology of categorising the grading of hadiths. This means which hadith is authentic, which is accepted, weak, fabricated, and so on.
It is for this reason that there is no specific book both Shi'ah and Sunni scholars would agree on. Yes, there are certain hadiths, in fact many of them, that both Schools would agree on. But not an individual book as a whole.
As for an objective seeker of truth, it is imperitve that one adopts a correct unbiased approach to research into factual information, and read as much as they can from all angles, and ask the Almighty to inspire them, open their inner eye, and guide them to the truth.
And Allah knows best.