The reason why those lights would seem to be of less quality as they operate in the DR, its due to the remarkable hours of operations vs the amount of time they output overseas.
A lights-out event overseas is mostly a mere minutes to 2 hours, a lights-out in the DR can be half a day and more; as such the batteries are depleted to the core and once that happens damage occurs, rendering the unit useless to recharge.
The same goes for battery operated tools, the power output in the DR fluctuates most of the time; even during normal operations the voltage will surge or decrease too often. Electrical noise is a killer of battery operated tools as well.
If you want to get the most out of your battery operated devices in the DR, using some devices like an APC back-up to regulate power and conditioning is a must, especially when recharging devices from the outlets.
You can add line conditioners to your home electrical panel to avoid costly damages because of power spikes and noise.
I currently employ an "inversor" in my home coupled with an automatic power generator, but I have almost all electrical devices connected to an APC with line conditioners in most lines from my service panel.