I still think there is a benefit to resigning over termination pretty much no matter what, and programs prefer it in almost every case because when you resign you lose various legal rights to challenge, whereas termination does theoretically open the door to certain types of actions ranging from appeals to lawsuits that most programs prefer to close the door on. It doesn't matter what you intend to do, it's just a fact what each path leaves open or closes legal liability-wise, so programs prefer the resignation in most cases. Also, theoretically it looks better for them for residents to "choose" to leave than to be the big bad program terminating. How that looks to future residents or even the ACGME. Because of that, you can potentially use the offer of resignation to negotiate some assistance for the next step.
No matter how nice your program is, I would still say "OK well it seems like the best thing for everyone involved is that I resign. I know this simplifies this process for everyone, so I ask in return a letter of recommendation to X specialty from the PD, and if these attendings agree to write one, a letter from them as well, to help me move on to a specialty that is a better fit for me."
This is a reasonable exchange. If they don't want to do this, I would consider an attorney for the purpose of getting those things in exchange for a resignation.
Don't go with the flow if the flow is them wanting to terminate you and give you no help moving on.
I have heard of WAY too many residents that went with the flow, didn't want to rock the boat, didn't want to formally ask for anything, that didn't get on paper getting these recommendations, that just signed where the program wanted for a resignation or didn't fight a termination or didn't offer to resign in exchange for letters instead of termination, basically that were relying on the "good will" and good intentions and nice words from the program, that got totally boned by their program. Anything from dragging their feet providing any proof of training to not providing a letter to badmouthing residents on the phone to other programs.
I'm not trying to say get all litigious and piss off the program. But if you don't use the chance of promises you can make on paper to get you some promises on paper, you're just at their mercy. Which could be fine for you, or could be awful. It feels better to walk away with negotiated letters in hand.