Information regarding which build to use is further down, but to start I'll briefly explain why there are two builds. Since the release of Qt 5.7.0 on 16 June 2016, GTK theme emulation has been broken in Qt. This has been reported as a bug, and has been assigned P1 priority, but has yet to be fixed. As such, applications built with Qt 5.7+ will not use your GTK theme on Linux. To illustrate this, here's Inviska Rename 5.0 built with Qt 5.6.3, which is correctly applying my green GTK theme:
Now here's Inviska Rename 5.0 built with Qt 5.12.2, which doesn't use my GTK theme, and generally looks a bit crap:
Since GTK theme emulation isn't implemented in Qt 5.7+, I have continued to use Qt 5.6 for my Linux builds. However, when testing the latest builds I discovered that the UI no longer renders correctly in Ubuntu 18.10:
Building the application with Qt 5.12.2, I found it appears in a usable state Ubuntu 18.10, though without GTK theme emulation:
It seems that Qt 5.6.3 may be reaching the end of the road, and may stop working on the latest Linux releases. To accommodate users on those releases, I have done additional builds with Qt 5.12.2, but GTK theme emulation will obviously not work in those builds. For that reason the Qt 5.6.3 release remains the recommended release if it will run on your system.
I've tested the latest round of releases (Inviska Rename 5.0, Inviska MKV Extract 7.0, Inviska MKV Info 7.0, Inviska ASS Stripper 5.0) on a the below distributions, in each case using the primary desktop environment for the distribution. Next to each I've offered guidance on which build to use.
For other systems, I'd recommend trying the Qt 5.6.3 build first, since that includes GTK theme emulation. If you experience rendering issues you can just remove it and install the Qt 5.12.2 build instead.
I don't understand why the they removed GTK2 theme emulation in Qt 5.7 and replaced it with nothing, or why they refuse to put GTK2 emulation back in while they work on GTK3 emulation, assuming they're working on it at all. It seems the Qt Company is now more focused on embedded applications, like digital car dashboards, rather than desktop applications. I'm not sure what that means for the future of Qt, though it is rather worrying that GTK theme emulation remains broken after three years.
I've included a comment box below in case anyone has anything insightful to say on the matter of Qt GTK theme emulation.