I was surprised to discover that Americans do indeed use the dialogue spelling when talking about a conversation.

Using the American English corpus:

Ngram

The graph for the British English corpus is very similar in appearance.

Historical data isn't very useful for a new concept like a dialogue box.

What we see for 2000 is:

• Dialog box
  • American: ~0.00240%
  • British : ~0.00045%
• Dialogue box
  • American: negligible
  • British: ~0.000050%

British people do use dialog, but usually it's when they're making concessions to American readers.

For what it's worth, my British spellchecker doesn't recognise dialog at all.

I was surprised to discover that Americans do indeed use the dialogue spelling when talking about a conversation.

Using the American English corpus:

Ngram

I search for "dialog with" here, because that's a word sequence that would only be used in the sense of "conversation with", and won't match "dialog box".

The graph for the British English corpus is very similar in appearance.

Historical data isn't very useful for a new concept like a dialogue box.

What we see for 2000 is:

• Dialog box
  • American: ~0.00240%
  • British : ~0.00045%
• Dialogue box
  • American: negligible
  • British: ~0.000050%

British people do use dialog, but usually it's when they're making concessions to American readers.

For what it's worth, my British spellchecker doesn't recognise dialog at all.