Detail would be presumably lower due to less control of mic position and due to the higher noise floor of the room.
Imaging is a function of mic position and mixing. It could be seen as improved or worsened: depending.
I think one nice thing about live recordings is that less is done to "clean up the mix". The fact is that, especially for those who like to go out and listen to live music, many sound engineers make choices that are deemed detrimental to the music. Whatever the physical limitations imposed by live recording; the loss of post processing is viewed (by many) as a good thing.
Personally, if the sound engineer has done a good job, I usually prefer the non-live recording for exactly some of the reasons you list; but it's not a universal preference.