I always use RELUs actication functions when I need to and I understand limitations of ELUs. So in what situation do I need to consider ELUs over RELUs?
ELU does not suffer from from dying neurons issue, unlike ReLU. While ELU can help you to acheive a better accuracy, it is a slower than ReLU because of its non linearity in its negative range.
Choosing a right activation function totally depends on situations but you need to also consider other similar types of activation function such as leaky ReLU.
Check this link out. It could be useful.
The answer above makes some great comparisons/trade-offs. To help address the non-linearity issue with eLU units that the previous answer brings up, you can also use Leaky-ReLU units, which are linear in both the positive and negative range, and piecewise-linear across the whole real domain.
Please see the link here for more details: https://qr.ae/pNsatH.