This is an interesting question, as I would not automatically think of these two wonderful novels in relation to each other. I have included the links below to the enotes sections on both novels, so hopefully that will help you further think through the question. Here are my initial thoughts, however.
I think the main connection we can establish between the two novels is the way that Offred and Holden are both presented as outsiders in their respective worlds. Offred is clearly an outsider, both in terms of her role as handmaid, but also because of her rebel sympathies. Likewise, Holden has made himself an outsider through his belief that everybody else is a "phony." I would say that this is the main connection between them, and any essay comparing these two novels would have to focus on how the central character operates in their respective world as an outsider. Of course, Holden finally manages to become included in his world as he realises that he does have attachments and that companionships and relationships are more important to him than isolation. The ending that Offred gives us is more ambiguous as she is clearly facing an uncertain future, trapped on the fringes of society and bearing her and Nick's child. She has not moved from isolation to inclusion in the same way that Holden has.
I can't think of any other similarities apart from this central idea about isolation. There are of course plenty of differences between these two texts, but hopefully my ideas will help you to analyse the question further. Good luck!
Hi, I'm doing the exact same thing as you and I'm tyring to connect the two, can help me out and tell me what comparisions you made? I have to find two quotes in both books and compare them and find similarities, thanks!