I think you'll find it's that particular monitor's Freesync support that is lacking not Freesync itself.
Because Freesync is open source adaptive sync it is up to the monitor manufacturer to use components with good quality Freesync compatability,
After looking across LG's entire Freesync range it seems that they do not use the right panels,
Add to that how at the moment the 38" panels do not seem to be capable of supporting the full Freesync range and a poor experience is to be expected.
I had my heart set on a 29" LG ultrawide before Freesync was a thing and once Freesync was announced I decided to wait for that before buying an ultrawide monitor.
When the first LG Freesync ultrawides appeared I held off because the working range did not go low enough.
Today's LG Freesync monitors are lacking in the two most important ways.
One is how wide the Freesync working range is and the other is supporting LFC (Low framerate compensation).
You bought a monitor with a small working range and no LFC.
In comparison if you had bought the 34" Acer Freesync equivalent to your Acer G-sync monitor you would have got a much better experience with a range that starts at 30 hz and supports LFC.
It seems that the 38" panels are not yet capable of providing the full Freesync experience.
If you scroll down this page and pick the monitor option in the box you'll see the relevant data
http://www.amd.com/en-us/innovations/software-technologies/technologies-gaming/freesync
This is how the Freesync tech on the LG 38", Acer 38" and Acer 34" compare
This graph shows the important points mentioned.
Range
LFC support?
LG 38"/ ACER 38"/ ACER 34"
52-75/ 48-75/ 30-75
No/ No/ Yes
In my opinion these are the two most important features for Freesync,
It is where G-sync has total control of a G-sync monitor and where Freesync is at the mercy of the monitor manufacturer.
As we can see both the 38" Acer and 38" LG monitor's are in the same boat with a working range which does not go low enough,
That along with having no LFC when the fps in a game drops below the working range is why your Freesync experience is not how you hoped it would be.