Can't comment on specifics since I've only got one photo printer but a couple of general points.
Firstly, I would never use cheap cartridges, only genuine ones. This is because I did try one once and swapped it for a genuine one PDQ because the colour was off (significantly - probably dealt with by calibration but not worth it), that colour faded fast, even in a sleeve (which would have made any effort calibrating for the ink a waste of time...) and there are loads of horror stories (first hand as well as "I read it on the web") about 3rd part inks blocking nozzles (not a cheap fix).
Secondly, I would look at A3(+) printers if you have the desk space for one. An A3 printer can print 6x4 prints but an A4 printer can't do A3!
There are reasons Epson and Canon have the lions' share of the market, not the smallest of which is that they simply produce better and longer lasting inkjet prints than the others.