For the typical user the compatible ink cartridges make for an excellent alternative. Every one of the cartridges that are offered for sale by companies should come with a guarantee of the quality of the output and also the lifetime of the cartridges. There have been tests where standard high resolution pictures have been printed onto 125GSM photo gloss paper and print using the originals after which flush the print heads out and run the identical process while using compatibles. The results were then stuck onto a wall to test for fading over a period of time. The conclusive response to the question ‘are they as effective as the originals’ is yes, and based on a price/performance ratio they're more than satisfactory, and some could even be tempted to state that they are excellent for the service you will obtain.
One final question, is there a difference between compatibles and refilled/remanufactured? The reply is fairly simple even though the technology behind both types of printers is quite complex. Epson, Canon and Brother all create a printer with an integrated print head, so when you change the cartridge all that you are changing is an ink tank. These days printers all use individual ink tanks for the various colour inks (up to 10 different cartridges in certain high class printers) meaning that when one colour expires you simple replace the empty cartridge.
If you examine an HP Cartridge you will see immediately that it is not likely to degrade and decay inside our landfill sites very quickly, in reality it is believed that it's going to take 10,000 years for them to decay so cartridge recycling is a huge thing, but you must be aware that the only cartridges which are currently worth the expense of refilling are the types using the integrated print heads i.e. the HP/Lexmark/Dell types. The Epson/Canon/Brother cartridges are merely ink tanks and therefore are not generally recyclable.
So my final answer on this debate is that the compatibles are often fit for purpose. If you're printing general office/home documents then save your valuable money and employ the compatible ink cartridges for all your printing requirements.