Learn English – the difference between ham, bacon, and gammon

Neither is more correct than the other. They're both common words. In fact, they're sometimes different words. For instance, to oblige someone is to do something for them that they want you to do. "She asked me to pick up dinner, and I obliged her by getting some lasagna from a little Italian place down the street."

That's not the same as obligating someone, which means to make them HAVE to do something (or feel that they have to). "Although the statue was meant as a birthday gift, he obviously felt obligated to get me something expensive in return, despite my protestations."

There is a dialect aspect to it as well. What's wrong with "obligate"? In US English nothing is wrong with it. In Australian English everything is wrong with it. Here's how I'd have put it.

"Although the statue was meant as a birthday gift, he obviously felt obliged to get me something expensive in return, despite my protest."

In my dialect "oblige" is fairly common but "obligate" is never heard. The distinction that Uriel mentions is not made in Australian English. We use "oblige" for both meanings.

The only real justification for seeing dialog as "American" is that there are many words where US spelling seems more "logical" than British - largely thanks to Webster, though so far as I know he never addressed this particular issue.

Paraphrasing grammarist.com's entry on another such word: all early editions of Noah Webster’s dictionary list catalogue, but by the 1890s catalog was commonplace in AmE texts (Webster often gets credit for changes he played no direct part in).

There aren't many written instances of dialog prior its rapid uptake by software-oriented writers, but here's one from 1910 Transactions and proceedings of the American Philological Association, where one might reasonably suppose the author to be perfectly literate.

I think it's just that on average people involved in technical writing are more inclined to ignore precedent and go for what seems to them the logical spelling. Consequently we see the short form much more often in computer contexts such as dialog box, leading many people to suppose there are in fact two different words involved (or at least, that the word has two different spellings dependent on context).

It seems to me usage is currently in a "transition phase", but most likely the shorter form will continue to encroach further into traditional, non-computer contexts, and will eventually be seen as standard for all contexts (but for most people, particularly Brits, this hasn't happened yet).