Once you get past the commonalities--durability, looks, cost--you have to confront one factor that is found in no other area except the basement: massive amounts of water.
Water is prevalent in bathrooms and it will quickly ruin the wrong flooring. With that in consideration, from best to worst, your floor covering options for the bathroom:
1. Porcelain or Ceramic Tile
Summary: Porcelain tile is the best of all worlds for bathroom flooring--waterproof, stylish, and cost-effective.
Like stone, porcelain tile can achieve a rich, textured, solid feeling. Like vinyl, it is waterproof and is fairly inexpensive. Like wood flooring, it looks great.
But should you choose porcelain or ceramic tile? Is there even a difference?
Porcelain is part of the ceramic tile family with one slight difference: water absorption. The Porcelain Tile Certification Agency (PTCA) certifies types of tile as "porcelain" if they have a water absorption rate of 0.5% or less.
If this is a half bathroom or powder room, you will not need to purchase porcelain tiles because there are no bathing facilities.
Because there are so many different types of ceramic tiles, you can create the exact floor you want. You can even find ceramic tile that looks like wood or stone.
Individual tile comes in sizes between 4" x 4" to 2' x 2', and in a wide variety of shapes such as octagonal and hexagonal. Smaller mosaic tiles are pre-mounted on plastic mesh sheets, so you do not have to individually set each tile. With tinted grout, you can be even more creative.
Best of all, tile cleans up well and bravely resists even standing pools of water.
Like stone, tile is cold (though radiant or heated tile is available.
Tile can be slippery. But texturing solves that problem. Smaller tiles are less slippery because more grout is used and the grout acts as a non-skid surface.
2. Vinyl: Sheet, Plank, or Tile
Summary: Reasonably good aesthetics, supreme practicality.
Vinyl is the most popular choice for bathroom flooring for several reasons. Vinyl is very much a do-it-yourself job (you can install vinyl tiles in a weekend, easily). Plus there are thousands of style options.
Sheet vinyl flooring is your best option if extreme amounts of water are expected, such as in children's bathrooms or laundry rooms. Gappy and poorly laid seams are floor killers. Sheet vinyl may have as few as zero seams in a small bathroom.
Luxury vinyl plank flooring comes in narrow widths (about 5") and long lengths (up to 48").
Luxury vinyl plank is very easy to install.
Sheet vinyl is difficult for the do-it-yourselfer to install.
3. Natural Stone
Summary: Good choice, but only if you can afford it.
There are few moisture problems with marble, granite, limestone, and the other stone flooring options. Stone is mid-level is this list and not at the top because of a number of issues.
The first one is that it is cold. The second issue: it tends to be slippery. This can be solved by having the stone textured by sandblasting or by purchasing naturally textured stone, such as slate.
But the main issue that pulls this bathroom flooring option down is cost. Real stone flooring is by far your most expensive flooring option.
4. Engineered Wood
Summary: Better than solid wood, due to engineered wood flooring's dimensional stability.
Engineered wood has a plywood base that holds up well against moisture. And it looks terrific because the top layer is real wood.
If you insist on natural wood in a bathroom, engineered wood is the best choice.
Summary: Laminate will work in bathrooms if you take precautions to protect the wood base from moisture.
Surprisingly, laminate flooring is a better bathroom flooring choice than solid hardwood. Laminate flooring is no more than resin-impregnated paper atop a wood chip base. The surface of laminate plank is actually a photograph of oak, cherry, slate, marble, or any other wood or stone.
On top is a clear coat called the wear layer, which is amazingly strong. DuPont RealTouch, for instance, warrants the wear layer on its line of laminate flooring for 30 years.
With tight seams between the planks, it is difficult for moisture to work its way downward.
Laminate is easy to clean, too. But laminate still has that wood chip base, and should it happen to contact with moisture it will expand and bubble and the only way to fix it is to tear it out.
Waterproof laminate flooring is an idea that has not yet come to fruition even though several manufacturers have tried.
A slightly better bathroom flooring choice than carpet, solid hardwood looks great and feels warm under foot.
But moisture kills solid hardwood. If you absolutely have to have solid hardwood in your bathroom, make certain it is perfectly installed, with zero gaps for moisture. This means hiring installers--unless your day job happens to be that of a hardwood floor installer.
Summary: Never a good idea.
A horribly bad choice for bathroom flooring. Moisture and carpeting do not mix. However, if you still must have carpeting in your bathroom, make sure the pile is low and the material is 100% inorganic (like olefin).