The Irresponsible Captain Tylor is one of my favourite anime. I got the original R1 DVDs (2002), then the R2 DVDs (2003), then the R1 Ultra DVDs (2005) and finally after so many years, the R1 remastered DVDs (2009) too. It is only natural that I add the screencaps here to compare.
You can still view the original page.
R1 remastered vs original
The remastered DVD release beats the original hands down.
R1 remastered vs R2
It is clear I got the black level wrong when I captured the R2 screenshots.
The R2 steps through the eye-catch very nicely, being 24 fps progressive. The R1 breaks due to 3:2 pulldown. (Nothing a deinterlacer can't fix. But why have it in the first place?)
Busy scene
Close-up character scene
Grain is comparable.
Background art scene
Scene transition
Same splice marks.