Both and how the ink reacts to the paper is important as well.
Assuming you are using decent inks/paper, you also need to use a colour-managed workflow, so that what you see (on the monitor) is (roughly) what you get on the printer colour wise.
Accurate and vivid colour also typically requires the use of a proper printer profile that is specific to the printer/paper/ink combination you are using.
Most serious photographers use pro-grade printers like the 2400 and on up, since you can get decent inks, paper and most importantly profiles for these devices. That's likely not the case for inexpensive consumer-grade printers (for example, I haven't found any profiles for my wife's Canon printer that we got at Costco).
I think you'll continue to be disappointed if you stick with inexpensive consumer-grade printers and cheap supplies.
Just my 2 cents worth...
I was afraid I would get an answer like this, so I assume it is time for me to change my printer... Apart of that, I have to ask again and always hope someone would be so kind in finding an answer for me, will there be any real differences If I get UT-R2 B&W ULTRATONE CARTRIDGES FOR THE EPSON R200?? Of course, I will try to find the best paper around, but will the ink change make such a big difference?
Now, I am thinking of getting a R2200, or R800 printer, I don't care about picture size, as I print only in A4 format, so, will they be ideal pro-grade printers for me to get my so sought after vivid and brilliant glossy covers?
All the best,