OK, I have close experience with both as an academic in the humanities. In terms of departments - they're both excellent, and your DC will get an excellent education at either. But the feel of each course is different, so your DC needs to have a good look at each department's website to look at the core compulsory courses, and the range of options. Although don't count on each & every option being available - it's dependent on staff availability & numbers etc. See what's on offer as a student there - not just Open Day stuff, but delve into the actual website. See what the staff specialisms are, and what is taught, and how it is taught. You can usually get a lot of information that's used everyday by students on the course now - a lot of info is not password protected.
So ... in my view, the big difference will be the places and the campuses. Both are green field, slightly out of town campuses. Both a little like villages. Both spectacularly beautiful in different ways.
Lancaster has close connections to the North and Scotland. I always notice that there are a lot more students who consciously identify as northern fine by me I'm a northerner Frankly, from the point of view of an academic, the students are far less entitled and whiny.
Royal Holloway students tend to be from the south, and like it because it's near London, but not in London. Students are much more 'yah' I'm afraid - but that's from an outsider's point of view as a tutor, I'm an observer butt an outsider to student life! 
Although Egham's very pleasant, frankly there's not much going on there but I'm an exiled northerner But, there is the easy access to London.
But Lancaster is 40 minutes from Manchester and an hour from Liverpool, and two hours to Leeds. Fantastic cities and then there's the Lake District & Scotland.
Both are very safe campuses and towns. Lancaster of course much cheaper, but if your DC's friends & family are in the south, the trainfares are more expensive.