This is very hard to answer and actually a very interesting question and it actually differed from one country to the next. For example in the United States you see newspaper advertisements for daguerreotypes continuing into the 1860s, whereas in France and Britain they had died out in the previous decade.

As to the pros and cons of each, here are some specifics: Daguerreotypes

Pros:

-Beautiful -Truer tones than tintype and ambrotype images were capable of. In that the whites were whiter rather than a pale brown or yellow. -More durable than paper photography. -Don't fade in light.

Cons:

-Time consuming to produce with more costly materials. Required a silvered copper plate painstakingly polished to a mirror surface. -Difficult to view, they require the right light and a dark surface to reflect against to view properly.

Ambrotypes/Tintypes

Pros: -Cheap, they are direct positives like the daguerreotype process and so don't require an additional printing step. For this reason they survived through the 1890s widely, and continued on at carnivals and such into the 1900s. -Viewable in any light. They don't have a reflective quality like dags and so are easy to view. -Photographers at the time advertised ambrotypes as longer lasting than daguerreotypes. This was a really questionable assertion...

Paper Printing (Albumen, Salt Prints etc from Wet or Dry plate negatives not considering Calotypes/Talbotypes from paper negatives)

Pros:

-Reproducible in multiples easily. -Easier to tint and color (some colors just don't 'take' on a daguerreotype surface as well. -Easily viewable in any light.

It is actually sort of curious why daguerreotypes held on the US so much longer than in other countries. This is really up for debate and an unsettled question in the field. I would attribute the US fondness for cased images to romantic cultural reasons, but who can say.