edited slightly due to Company B's confidential offer. You'll want to verify with the confidentiality clause that my answer doesn't violate it.
It depends on your goals.
If you want the best possible offer from Company A, give them very broad ranges.
Total year 1 compensation is in the range of $300k.
The risk is that Company A has sticker shock and you get no offer.
If you want a definite, though possibly lower, offer from Company A, don't tell them anything.
I'm not at liberty to say more than that their offer was competitive. (they persist) The offer is confidential, and I think it's premature to negotiate salary as you haven't presented an offer yet. (they still persist) Your unwillingness to respect my obligation to not discuss the other offer at this time makes me seriously question whether your company would respect me as an employee.
note it should make you seriously question their ethics and how they would treat you as an employee
The risk is that Company A comes in much lower. Though your counter to leverage your exisitng offer.
I think the $20k starting bonus and $200k in SO is very reasonable. If you can offer $110,000 in base salary, I will accept that offer right now.
You could end up with your preferred company and more money. Though they may not be willing to match. Then you have to decide if your preference is worth the monetary delta.
Since your comment mentions you prefer Company A, the second answer is lower risk, higher reward.
Edited to steal some wording from @HireThisMachine's answer