How to "best" convert Adobe RGB images to sRGB

Doing it using Edit > Convert to profile allows you to choose the rendering intent. That’s how I'd do it, you also get the opportunity to preview the changes and MAYBE alter the original still in Adobe RGB before converting. 

Moving images to a smaller colourspace can "clip" detail in areas of high saturation. The histogram will reveal clipping 

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

To convert first, I mean:
Open the Adobe RGB image > Edit > Convert to Profile (sRGB Profile ...) > Export > Save for Web > Embed Color Profile, Convert to sRGB.

 

I have looked at both images exported with the 2 methods, and they are visually identical, but reading the histogram data the data changes slightly.

 

Thank you!

By @alexsalvatoretrotta

Is that a typo? Why convert twice?

Any colours that exceed the sRGB gamut will be clipped.

Standard sRGB profiles only have a relative colorimetric table. You could try an sRGB profile with a perceptual rendering table (generally found in output printer profiles, not working space profiles):

https://www.color.org/profiles/srgb_appearance.xalter

https://www.color.org/srgbprofiles.xalter

Once converted to sRGB using both methods and viewed in a web browser, you can then make your own call.

The conversion uses the same colour engine whether you convert in Save for Web or in Edit > Convert to Profile.

However Convert to Profile offers additional control over the rendering intent. This affects how colours that are out of gamut, i.e. colours that exist in Adobe RGB but cannot be contained in sRGB, are treated. 

The two options applicable here are Relative Colormetric and Perceptual. Simplistically, Relative colormetric moves out of gamut colours into the smaller gamut, Perceptual does the same with out of gamut colours but also moves some in gamut colours to maintain a perceptual difference between them. Which is best depends on the individual image.

You can turn on proof colours and see where those changes as you switch proof on and off and then adjust the image accordingly.

Dave