Happy to have the question re-written by anyone with more experience than me (which doesn't exclude many!!). The reason I asked it like that was because at 6"x4" I'm always struggling to see the finer detail on prints from my iP7250. When I print the same photo at A4 size (8.27" x 11.69") the detail is naturally much easier to see so therefore presume that any discrepancies between the current 9600dpi printer and a new 4800dpi printer would also be easier to see.
I don't do anything special when printing, just use the full-size image exported out of Lightroom at 72dpi and print using Canon's Easy Photo Print.
Let me address your observations. Let us start with and assumption, that your photo file was shot with 1200 x 1800 pixel camera. Then we change the assumption for the last two situations, and use a camera which can switch between 1200 x 1800 pixel count, or to 2475 x 3710 pixel count image.
- When you view your 1200 x 1800 pixel image printed to 4" x 6", your photograph has 300 PIXELS per inch (1200pixels / 4" = 300 ppi);
When you view your 1200 x 1800 pixel image printed to A4, your photograph has about 145 PIXELS per inch (1200pixels / 8.27" = 145 ppi);
your eye can perceive a different in quality and the reduced detail in the 'magnified' view of 145 pxiels per inch print.
- If instead, you view your 1200 x 1800 pixel image printed to 4" x 6", your photograph, your photo has 300 pixels per inch
Or if you shoot a 2475 x 3710 pixel image in your camera and print it to A4, your photograph, your photo has 300 pixels per inch
your eye perceives the two as 'same quality' as each other, since the 2475x3710 image has captured twice the detail resolution in each axis of the photo, compared to to 1200x1800 image.
- Lastly, if you shot a 2475 x 3710 pixel image, and blew that up to 4" x 6", your human vision has a limitation that prevents it from detecting all of the detail in the print! But when you print that 2475x3710 pixel image to A4, the detail is about twice as large, so you can detect visually some of the buried detail which was ALWAYS PRESENT in the print but your eye could NOT SEE at the smaller size.
Now, back to the topic of 9600 dpi (drops per inch of ink from the printer) vs. 4800 dpi (drops per inch of ink from the printer)...
Your printer, at its highest 'quality', sprays a pattern of dots to make your eye perceive different hues assigned to a pixel. One pixel might have 960 dots of ink vertically and 960 dots of ink horizontally, so that your eye sees 'avacado green' for that pixel. Your printer, at the lower 'quality' sprays a pattern of dots to make your eye perceive different hues assigned to a pixel. One pixel might have 480 dots of ink vertically and 480 dots of ink horizontally, so that your eye sees 'avocado green' for that pixel. (Regardless if the print was 4" x 6" or if it was A4, the dpi of the print is the SAME for both size prints unless you change the 'quality' setting in the printer driver software!)
Can your eye see the difference between 9600 and 4800 dpi? I don't know...my printer maxes out at 4800 dots of inch per inch, so I cannot do a test and then tell you if I can perceive any difference.
And that is what I earlier suggested to you to TRY IT OUT FOR YOURSELF, and make a judgement about your own eye's ability to detect any difference.
If you cannot see a difference (remember, print size does NOT MATTER, when talking about inkjet ink density)