At different time periods and in different countries / academic cultures, either one or the other was more popular to denote (essentially) the same thing.
I won't go into the historical details (in which I am not too well-versed), but here's an example: In my own Alma Mater, for example, they used to award D.Eng. and D.Sc.'s, and no (?) Ph.D.'s until the 1980s or so, but at some point they switched, and these days everybody gets a Ph.D.
Did this matter to anyone? By and large, no. I've never heard anybody complain about the latter or the former having caused him/her any trouble being recognized. So while it is theoretically possible there will be some kind of issue, it doesn't matter.
My personal opinion is that it's a shame we are losing these discipline-group-specific titles and going with something generic - even if it has older historical roots. So I would go for D.Eng.
Also, if your friend has a signed official letter saying something like
We can award you with either a Ph.D. or a D.Eng. and we consider them equivalent in your case
then she can use that specific letter with whatever degree she is awarded, if any questions come up.