I tend to prefer Lowes. IMHO, Lowes stores tend to be cleaner, items are in place, better, and store layout makes it easier to find things than at HD. I do shop Home Depot for a few items, particularly Milaukee tools and Rigid utility vacuums.
The first home improvement superstore close to me was a Lowes, so I started shopping there. But upon a friend's recommendations, I started trying HD, but on a constant basis, I wouldn't find what I wanted, or was disappointed with the selection or quality, and I would walk out without buying anything. My wife started harassing me, asking why I even bother going to HD, as I always come out empty handed. It is still a standing joke between us.
Another down side to HD is ceramic tile quality. A few years ago I was at a tile store buying tile for a small project. I mentioned that I was going to pick up some of the tile for the pattern I was going to do, at HD, as the tile store didn't have exactly what I wanted. The tile store manager cautioned me that I needed to be aware that the tile sold at HD is thinner, and so when mixing with other tile, it will be recessed a little. They were right. I still used some HD tile on that project, but I no longer shop HD tile.
There are no Menard's in the West. Even if there were, I would still primarily shop at Lowes. I've shopped Menard's with my son, who lives in Kentucky. They are nice stores in some ways. Fantastic selection. But the stores are too big, resulting in having to take an awful long time to fine what I need, get it paid for, and get home to my project. And it's totally unnecessary for Medard's stores to be so big. They are filled with a lot of junk that is unrelated to home improvement. Like books. What the heck are books doing in a home improvement store? In addition to selection, the only other thing I like about Menard's is price. From what I've seen, they tend to be a little lower priced than Lowes or HD. But not enough to make it a preferred store for me.
Oh, and as someone else mentioned, I do love the Lowes phone app. It is so convenient to have it tell me the aisle, shelf, and location to find an item.
And I love buying items online at Lowes for store pickup. It is so nice when they call and tell me that my item has been pulled and is ready for pickup.