The meaning of both phrases is the same, the clause order is merely reversed. As regards the Satanic prayer, it is highly unlikely that this has any bearing on modern translation choices. The word ordering has simply been modified to make it easier to understand in modern English.
What is interesting is that most modern translations do not include this clause at all in Luke 11:2, as it likely was not original to the text:
"Most MSS (א A C D W Θ Ψ 070 Ë13 33vid Ï it) read at the end of the
verse 'may your will be done on earth as [it is] in heaven,' making
this version parallel to Matt 6:10. The shorter reading is found,
however, in weighty mss (Ì75 B L pc), and cannot be easily explained
as arising from the longer reading" (NET Translator's Note on Luke
As an additional note on any influence from the Satanic prayer, they generally say the entire prayer backwards (word-for-word, not clause for clause), so this is a misunderstanding to begin with. The only references I could find to this were various blog posts of dubious reliability that cited no sources nor defended their assertions, and they did not have an issue with either wording in your question (nor were they even in reference to the same passage). Their primary contention was with the Message Bible's wording: "as above, so below" in Matthew 6, and they were clearly advancing a KJV-only agenda (which is a doctrinal controversy - not a scholarly one).