It could also pay to compare them for their differences. Buddhism has precepts to rigorously follow and a morality and honesty. The non-dual is more based on an experience of peace and open space, even before any notion of a me as an individual.
Without a distinct individual identification, precepts and a morality might seem like they are just made up concepts. They are distinctions created in man's mind. Who even knows how they were created because most of them are our inheritance and they were here before we remember. We simply adhered to them, knowingly or not. As they relate to the peace and open space, they are merely excess baggage and clutter. Many in the non-dual world kindly regard these Buddhist tenants as a sort of a kindergarten, or starting place that somehow gets you into a condition where you can find that spaciousness for yourself.
Let's consider a text which we all know, and see what we can make of it:
"When I see that I am nothing, that is wisdom."
"When I see that I am everything, that is love."
"In between these two, the whole of my life flows."
At first sight we seem to have two things going on here. This could be explained away and called paradox and such. But most important and irregardless of any explanation, is the interpretation given by the most common of listeners. The western observer (who is already in love with objectification), is going to twist and turn trying to deny that they see two states. I believe that we can see both non-duality and Buddhism within this quotation. Let's take a look.
1. The "wisdom in seeing nothingness" supports the Buddhist precept of non-attachment. But the non-dual adherent might be creating a "something" called a no-thing. What else can he/she do? Two thoughts will always create two things, that's how it works. Another solution is how long can you go without a thought? You definitely cannot force them out, and thoughts are part of getting around in a normal day. At best you're left with the two things, which you don't have to identify with. Whatever that could mean to each one of us?
2. "When I see that I am everything, that is love", now we seem to have two paths, one for the Jnana and one for the Bhakta. So maybe individuals are suited for different approaches, and I guess that it's said that they might end up with the same spacious viewpoint. Buddhism does have a precept of expressing compassion, which leads to love, so it acknowledges this statement too.
3. So here we have the non-dual listener (let's consider the common listener again, since they far outnumber the true knower probably by many thousands of times), who sees these two end points, which he/she aspires to as the highest truths. Since they do appear opposite, I guess you take your choice. The western man/woman loves to shoot for the best, so one of these two will definitely be the goal. All the messy stuff in between is left as only what needs to be overcome in order to get one of those results.
You can notice in your life, that rarely if ever do you find yourself as nothing, and more rarely as everything. There might be a time of warped experiences or deadened senses, and if those experiences are classified as pleasant, perhaps they will be taken as a proof that you can live in this bliss. But in general you will never find yourself as one nor the other. So is it safe to say that for all practical purposes and for the vast majority of human beings, these two principles are strictly concepts not verified by life?
4. OK, for a minute let's jump out of these three statements to discuss The Buddhist insistence on the practice of their precepts, before we return to attempt to bring it all together. When western man considers practice he/she thinks of mimicking a pre-set thought/behavior pattern with the idea that it might eventually rub off and become my nature. You might even make the excuse that it already is my nature, but for whatever reason, it doesn't appear that way yet. Volumes can be written trying to close that gap. Many Buddhists might take it the same way too, especially with store bought Buddhism or book learned Buddhism. There just are not the roots to innately know that I cannot behave in any other way, (than the precepts). So then trying and efforting and purification will be stressed.
5. But what is the main common ingredient of all of these Buddhist practices, non-killing, non-stealing, non sexual abuse, non-lying, loving kindness, compassion, charity, appreciative joy, equanimity? Every last one of these depends on, and comes onto your radar only when there is the other. It's in the family, in the community, in society. There is no such thing as honesty without someone to be honest with. Or let's say that closet honesty isn't honest. It is a flight of fancy. So every one of these precepts have to be expressed. That is always stressed in Buddhism.
To express anything you must be engaged with your fellow human. You can express, "good doggie" without a human, but what does that mean in your life? Deep insight into Buddhism is only about being engaged in society. You are offering yourself to society and the good of your fellow man.
It can't be all that real in a cloistered society. In western walled and gated communities Buddhism degenerates into endless purification and useless distinctions like not sitting on elevated chairs or sleeping on high beds. "Maybe my cushion is too fat, am I trying to be better than my brother?" Purify, Purify. But holding the other in love means everything on a horrific battle ground of a country like Myanmar. It's not hating a government battalion who just burned out an innocent village and laid land mines around it. It is a deep realization that there cannot be a successful struggle to end all struggle, which is an expression of thinking that is really unapproachable to the western mindset. It's "Get Real Buddhism".
6. Do you need to be engaged to feel that you are nothing? Is there engagement needed to feel that you are everything? I think not, that actually engagement is seen as a hindrance to experience these rarified states. So perhaps the major difference between Buddhism and non-duality is that one insists on works in society and the other insists that there is no doer, no one to do for or toward, and nothing that ever gets done. No engagement, flat out. (Of course our lives seem so rarely to work in that way?)
Engagement is an experience, with or without thoughts. Non-engagement is an experience, but only based on the thoughts of avoiding engagement and avoiding expression. It's only based on rarified dreams and concepts. Every thought does bring some experience, but how practical toward this life will it be?
7. OK back to our quote, we were left with the two end points, the two highest truths, and both are merely concepts. All the in between parts were the hindrance, or just the hump to get over to see these truths. Of course "In between these two my whole life flows", is the only thing that absolutely and always IS real. You can't pin it down though, because "it flows". So no concept can catch it.
This flowing reality is the only part of our quotation that is 100% engaged Buddhism. Don't be afraid, it is only your life. Sure it is risky. And it may take a non westerner living in the forest to really get what a blessing it is.