Definitely stamped concrete.

What style is your hown? The stamped design depends on if you're going for something modern/contemporary, rustic, traditional, etc. I personally like the idea of the slate look your husband wants. I also would consider maybe a wood plank look, something geometric, or to be super bold and modern, try the image below with the pebbles added between the concrete.Those are styles that are very popular right now.

gardengal what do you think of sand finish?

Fine. it's similar to the exposed aggregate but not as defined and smoother.

@Erin Morrissey, how is sand finish created? (It has never been common anywhere I've lived when I was there.)

A mistake that can happen with stamped is lack of experience with the installer. Good stamped can be gorgeous but bad stamped can be hideous ... which is why pavers are often thought of as a safer solution. There's all kinds of options with concrete.

We did a bluestone finish. We were told after the fact that we should be careful not to scratch it with the snow shovel. I was not expecting that. They do make snow shovels with a plastic edge, but we don't use the walk in the winter, so it hasn't been an issue. It also needs to be sealed every year or two.

interesting. we live in california, but i wonder what else you have to be careful about. we have a slate finish stamped concrete on floating steps on our front walkway but the backyard is a much bigger area

Stamped concrete uses surface color. It can be scratched off with metal tools, or chipped with a hard blow. And, of course, you'll see white below.