Depends. If you use a bootloader like grub that will put you in protected mode (The GDT is a bit undefined, but in general you can probably get away with just leaving it for simple programs). However, when you go to protected mode you lose access to the BIOS interrupts (and DOS interrupts if you're using them) and gain access to other features, so the range of things that are easy vs. hard changes a fair amount.
But if you're just planning on writing very simple text programs in ASM, then the only things that are really relevant is the text display, keyboard, and possibly disk/floppy. The text display is exactly the same (assuming the GDT from grub places it at the same location), but the keyboard is a fair amount more involved, and floppy is basically impossible (without writing a fairly involved driver). An IDE driver is surprisingly simple though (But still requires an interrupt, as does the keyboard). Both of these things are basically functions calls when you still have the BIOS around, so it does create a bit of a problem.
But if you're just planning on writing very simple text programs in ASM, then the only things that are really relevant is the text display, keyboard, and possibly disk/floppy. The text display is exactly the same (assuming the GDT from grub places it at the same location), but the keyboard is a fair amount more involved, and floppy is basically impossible (without writing a fairly involved driver). An IDE driver is surprisingly simple though (But still requires an interrupt, as does the keyboard). Both of these things are basically functions calls when you still have the BIOS around, so it does create a bit of a problem.