The modern HDD game installers are:
HDLGameInstaller (on console) + original disc (on console)
HDLGameInstaller (on console) + chip + copied disc (on console)
HDLGameInstaller (on console) + Windows utility (over the network) - best reliability, IMO
HDL Dump Server (standalone homebrew, or built into OPL) + hdl_dump or hdl_dumb (over the network) - capable of advanced operations such as making PS1/homebrew HDDOSD bootable partitions
hdl_dump or hdl_dumb (with disk connected directly to PC) - potentially best performance
WinHIIP is not recommended anymore (for installing games, at least) due to the above, more updated replacements (which do not attempt game-specific hacks that sometimes it gets wrong)