Compatible cartridge is a cartridge manufactured by third party manufacturers and designed to work in designated printers without infringing the patent of printer manufacturers.
A refilled product is typically not re-assembled, but merely opened with varying degrees of professionalism and is refilled with toner powder. While a compatible cartridge has 100% brand new components, assembled in state-of-the-art units. Refilled products typically suffer from low reliability, high failure rates and poor print quality, while compatibles compare with OEM standards in performance.
Reliability of compatible cartridges was a challenge till a few years back, but with advancements in technology, investing in R&D and refinement of whole process some manufacturers have achieved the benchmark of OEM performance.
In the official link of HP Printer Warranty below it is nowhere mentioned that printer warranty will be void if one uses non-HP cartridges http://support.hp.com/us-en/document/c01848047 It clearly states "For HP products using a non-HP toner cartridge or refilled toner cartridge would not affect the warranty of the product or the HP support contract that the customer must have had. However if printer failure or damage is due to the use of non-HP or refilled toner cartridge, HP will charge its standard time and price to service the printer for the particular failure or damage"
Unlike OEM cartridges Compatible cartridges are manufactured in different factories with different levels of automation, professionalism and choice of spares. To get the best product it is advisable to go with the reputation of the supplier.
Cost of cartridge although is an essential part but not the only factor to determine the cost of printing. You might find cheaper cartridges but when it comes to total cost of ownership of your printers which includes, yield, maintenance costs, transit damages, cost of inventory etc. we are definitely best