Here is a brief explanation.
A living will or a medical directive (and other various names) is used to give your desires if you are unable to make medical decisions on your own. It usually includes what your wishes are for things such as feeding tubes and life support machines and can designate one or more health care surrogates who can make those decisions for you.
A will is a document that is used to give away your property when you die. If you do not have a will, the intestacy law of the state of residence or where the property is located will apply and is also subject to dower/curtsy for distribution to spouses and heirs.
A trust is a legal device where ownership of property is placed in the trust and the trustee manages that property.
With this background, living wills would not have any bearing on ownership, transfer or possession of firearms. So the real question is whether you transfer firearms by will or by trust. I will first say that if your value is $1,000,000 or more, you need to have a trust. It gives the most control both before and after death. However, trusts are expensive and are legally very technical. Whenever i am approached for something that is going to require a trust, I always refer them to someone who practices primarily in that area.
Which means for most of us, transferring property by will is usually the best way to do so. It is inexpensive and, for most property, is very simple. In the majority of states, transfer of a firearm to a family member by will is not an issue. For those states like Illinois, it can still be done but is probably best to be done through an FFL so no local laws are broken, especially if it is an interstate transfer.
If you have any NFA regulated property, then a trust, more specifically a gun trust, would be the most appropriate device. I am familiar with gun trusts, but not well versed on them and would not attempt to draft one without partnering with someone who has done them in practice.