In the phonetic alphabet it's /e:/ vs. /ei/ and /o:/ vs. /ou/.

If you're an English speaker, you can be forgiven for a very stereotypical trait of the English accent. English speakers have a real hard time with the /e/ or /e:/ sounds as well as the /o/ and /o:/ sounds. Most English dialects don't have either a monophthong /e/ or /o/. Both the long and short tend to get heard as /eɪ/ and /oʊ/.

French enchanté /ɑ̃ ʃɑ̃ te/ is heard and borrowed as /ɑn.ʃɑn.teɪ/. German gehen /ge:n/ is heard as "gain" /geɪn/. And Japanese /o:/ and /ou/ both get heard as /oʊ/.

It's arguably a minimal pair in Japanese: 負う /ou/ (to carry), 王 /o:/ (king).

The main issues probably arise on official documents and stuff with financial impact.

Like how many people end up with the same romanized name while being distinct in other alphabets. Then discrepancies between the different systems because they usually are sloppy on the handling of these matters.

Now that most stuff is electronic, these small differences can have wider effects and be a PITA to fix.

They’re not the same. おう is discernible from おお, and the difference can be important.

That said, this is far from the most important problem in Japanese pronunciation for westerners, and at speed the distinction between them can become very subtle.

> What's the issue here?

You need to know previously the word to write from Hepburn to Kana when "ō" is present because data is lost in such transliteration from おう or おお or オー to Hepburn.

The internet is full of romanji written incorrectly with "o" alone when it should be "ou" or "oo" due "ō" ASCII conversion errors at one moment.

(The sooner a beginner embrace Hiragana and Katakana, the better)