Do these two sentences have the same meaning?
Of this spiritual world, our world is an imperfect image.
Our world is an imperfect image of this spiritual world.
The difference is in emphasis. The former emphasises the spiritual world and the latter our world.
When you compare something sometimes you look at them side by side and other times first the one then the other. Alternating, your first impression can subjectively affect your perception of the second (which is why optometrist agonise over lens comparisons several times over). Here the speaker/writer is trying to alter the ordering for the sake of that subjectivity in comparison.
Incidently the fact that thedefinite "this" is used implies there is context in previous sentences that mention the spiritual world that indicate it would naturally be the first point of comparison given enough detail. The second sentence would be used if you want to correct for this tendency.
Yes, they mean the same thing. But they are not of the same register, the same formality. One of those two is far more likely to be encountered in writing than in speech.
The latter sentence expressed the thought in a direct and straightforward way, almost pedestrian. It is the sort of sentence you might hear casually uttered by natural speakers in completely extemporaneous circumstances.
The former sentence varies the word order for rhetorical impact. It is more finely crafted, something to be used with forethought and planning such as in oratory, speeches, prayer, or in any sort of literature of a higher tone.
Compare these two sentences, whose ordering of formal first and casual second follows those of your own two examples:
Of English I know nothing; of Arabic, less.
I know nothing of English and even less of Arabic.
Which one of those moves you more?
Which are you more likely to remember?
And which will get you looked at curiously at the pub? :)