Eneloops have treated me well over the years. I use them in my camera flash on professional shoots. My headlamp for hiking. Flashlights. Whatever they go in you can trust they will work right.
There needs to be a preface, like this: *typically
Some items just do NOT play well with 1.2V. The good batteries, I think Eneloops do as well, will actually have a little bit more voltage than that.
The biggest thing - most battery-based devices are built for around 1.1-1.2v - alkaline 1.5v batteries drop from peak voltage almost immediately, and start going to around 1.4 and 1.3v and lower as they are used. Once devices stop receiving their absolutely minimum voltage, the battery dies. That's why dead batteries for some devices, can continue to work perfectly in other devices for some more time.
There are some devices out there that won't last too long running on 1.2v NiMH. NiMH holds voltage VERY well, and typically stays near peak voltage throughout life, but it does drop slightly. I think they usually get down to around 1.1v.
Generally, you never have to worry about that. I actually haven't encountered any, but I've heard of problems. Not sure if there are typical device classes where this is an issue.