As far as my level of understanding goes, the only difference between a 32 bit and 64 bit disassembler is that the produced assembler-code of a 32 bit disassembler is only using 32 bit assembly instructions, while a 64 bit disassembler also makes use of 64 bit instructions and registers.

My questions is, what are the advantages of using a 64 bit disassembler over a 32 bit disassembler?

Furthermore, if I want to disassemble a program compiled for a 64 bit machine, can I use a 32 bit disassembler like OllyDBG for that and what how would the output differ from a 64 bit disassembler like x64dbg?