Great generals are much more specific, they give bonuses only to certain eras. So a great general would give it's bonus only to units in the Classical and Medieval era.
On the other hand, Great Generals are game-changers now. They not only give +5 combat strength but more importantly +1movement. So imagine 3 movement archers, spearmen and swordsmen. With the new movement mechanics, they can move-and-attack onto rough terrain. Imagine combining a great general with some amphibious promoted units, not even rivers will stop them early game.
However, unlike other districts, the encampment does not give any yields. This means it tends to be ignored by most players so far. But once players realize how powerful the new Generals are, they will start to rush them.
Another factor in not going for generals may be that you can win your entire continent with 3 archers (and likely less).
Also note that not everyone will be getting a great general. Great people are now globally competed for; once the classical general is gone, its gone for everyone who hasn't gotten it. So it's important to be the first to get enough points for that great person.
In summary, you have some districts that are powerful but with weaker great people (think engineers or scientists) and some districts with weaker sites but game-changing great people.
p.s. Once a great general has outlived it's era, it can be used for a one-time boost: e.g. create a great work of writing or create an army.