I assume with serial uploader, you mean using the BOOT0/BOOT1 pins to enter "programming mode" and then use the serial connection to flash the firmware.
If you use it only to upload a bootloader, and use the bootloader to flash the firmware, I don't see the advantage.
The advantage of STlink (or any other debugger) is the ability to actually debug the firmware, as in, step through the code, look at register content, etc.