Sian
There are advantages and disadvantages to both options so they need to look at what works better for them.
I assume that she has not worked in the Tax Years 2015-16 and 2016-17?
These primarily revolve about how they are treated as a couple. In both cases, her wife's earnings will affect her ESA payments, I would expect them to have more money under UC but her wife will come under more pressure to increase her work hours and she might be sanctioned for failing to do so. There is no conditionality on the partner for ESA.
I suggest that they put their information into one of the online benefit calculators so they can make an informed decision.
www.gov.uk/benefits-calculators Providing the ESA claim is made before there postcode becomes a UC Full Service area then it will continue and they will not have to make a claim for UC.
Gordon