The tag that you want will depend on how you plan to use the time.
For example, if a doctor in a hospital wants to know when his or her patient was scanned, they usually want the “Study Time”.
If you want something more precise, the “Content Time” is when the image was generated (kind of a vague definition). In some situations, the “Content Time” will be different from one image to the next image, even within the same scan.
The “Acquisition Time” is a type 3 tag (optional), and it won’t always be present. I think it’s most useful for DERIVED images, since it indicates when the original data was acquired rather than just when the derived data was “created”.
However, if you need to do something like sort a 4D cardiac scan into the correct order, none of the above times will be useful, instead you want to know the “Trigger Time” which says where each image is in the cardiac cycle.
In general, the use of “time” in DICOM is going to be different for X-ray vs. cardiac MRI vs. nuclear medicine etc. Can you explain in more detail what you are using the time for?