Very open ended question. It is usually data specific. Usually if you ignore the pyramids, it will generate more overviews to cover for the data. The overviews increase the performance.
We already have pyramids for some of the source data . So my question if we remove the pyramids and rebuild overview . Is this going to improve the performance ?
The presence of the pyramids will affect how many overviews are created. If you remove the pyramids and then generate new overviews you are not really gaining much. I am not sure where you are going with this, but perhaps if you are looking to generate more overviews, you can use the define overviews to force more overviews to be created. This will give the image service more levels to choose from and increase performance. Perhaps you should take a look at this blog.
Thank you jeff and Eric for the reply .. The Blog was really good . It gave useful tips . Probably to make myself clear I am restating my problem ..
We Have Satellite images , elevation data in different file formats .. Previously While we created the mosaic datasets we built overview (Build Overviews) as well as the pyramids (Build pyramids and statistics tool) .. Now we are cleaning the mosaic datasets so this question came up whether Both pyramids and overviews are required for good performance of mosaic dataset OR Only Overviews are enough for good performance of mosaic dataset