TL;DR For the same (effective) aperture value with all macro methods, you'll get the same DoF, e.g. with effective f/16 and a "sharp spot" defined as 0.02mm, you'll get +/-0.32mm. Read on for a more detailed explanation plus a few caveats.

Projection geometry

With a 1:1 scale, you also get a 1:1 relation between the object displacement and the picture displacement, meaning that an object 1mm closer to the lens will get projected onto a point 1mm behind your sensor. The light that focusses there comes through a cone formed by the lens opening and this focus point. Only there in the focus point, all the light concentrates in one point and gives the sharpest picture. If the sensor isn't placed there, it instead sees a circular spot of light.

The bigger the displacement between the focus point and the sensor, the bigger the light spot gets, depending on the opening angle of that cone, and that angle directly corresponds to the aperture value.

E.g. f/1 is a 60° cone, meaning that the light spots grows by 1mm for every millimeter displacement ahead of or behind the sensor plane. With f/11 you get a 5° cone, meaning an 0.09mm spot for 1mm displacement, and with f/32 it's 0.03mm per mm.

With your desired 1:1 scale, the displacements also translate 1:1, meaning that a 1mm displacement at the sensor side correlates to 1mm displacement on the object side as well. (That's true no matter how you achieve the 1:1 ratio.)

Now then, how big is the depth of field?

That depends on two parameters:

• How big a spot of light do you accept as still being "sharp"? In the good old analog 35mm times, this was typically assumed as 0.03mm, being roughly equivalent to a 1-megapixel effective resolution. If you're using a crop-sensor body, then 0.03mm will be closer to 0.5 megapixel, and that sounds like rather poor quality. So, I'd go for a smaller spot size, maybe 0.02mm or even 0.01mm.
• What's the effective aperture value you'll use? Multiply your maximum spot size with this aperture value, and you get the depth of field (then multiply by two if you want both halves added, the part in front of the focal plane plus the part behind it).

Caveat 1 (aperture value):

Maybe you noticed that I used the term "effective aperture value", as that's not the nominal value you see on the display, or what you adjust the aperture ring to:

• With an extension tube, the effective value will become twice the nominal one. E.g. when setting to f/16, you'll effectively get f/32.
• The same factor two applies to the lens in retro position (with extension tubes or bellows to reach the correct position for 1:1).
• With a close-up lens (a secondary lens mounted in front of your base lens), the effective aperture value roughly stays true to the nominal value.
• With a specialized macro lens, it's can be anything between the nominal value and the factor two, depending on the inner focussing mechanics.
• With a tele-converter (one possibility you didn't mention), you have a factor of two, multiplied by an unknown (smaller) factor for the 2:1-capable macro base lens.

Caveat 2 (diffraction):

One nasty property of light is its nature of being an electromagnetic wave, resulting in an effect called "diffraction". The narrower you make the cone of light by closing the aperture, the blurrier the focus point gets. A rule of thumb is to multiply the effective aperture value with the light wavelength (roughly 0.0005mm), and then you get the size of the diffraction spot.

So, if you try to increase the DoF by closing the aperture maybe to an effective f/64, then not a single object detail will be sharp, you'll always have blurs of 0.032mm, even for details exactly in the focal plane.