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Option #2 only works in ArcGIS Server 10.0 (publishing mxd files).
I would choose to publish it as an image service (option #1), if you have that extension licensed in your ArcGIS Server. If you can put the mosaic on the web server (if there is room), it will be faster than referencing it from a shared directory.
On the other hand, caching the mosaic is much faster in terms of performance.
How about this in ArcGIS Server 10.9
Is cached service still much faster than mosaic published as images service?