In any school, historical culture and social environment play a large part in determining the overall educational experience. For these two grand old schools, it is no different. So the best approach to answering such a potentially explosive inquiry is to just state some facts. Disclaimer: my family has members from both schools (as well as others).
RGS has no feeder school (no, RGPS is not an affiliate). It has a high COP and hence an academically more homogeneous population. It is not unusual to expect these students to do well academically; as long as there is some relationship between skills required at higher levels and PSLE, they will continue to excel. RGS (like RI) suffers from not having a feeder school in the sense that the networking ties between individuals and generations tend to be weaker than those in premier schools which do have feeders.
MGS has a feeder school and comes from a family of Methodist schools. It has a lower (but still reasonably high) COP for non-affiliated entry and a much lower COP for affiliated entry. This gives it an academically more heterogeneous population. Since the primary school is in a generally more up-market area than most, it is likely that primary school admissions come from homes with above-average income levels. MGS (like ACS) has a strong social network that acts to conserve and protect a certain kind of culture and tradition.
In both schools, you will find a desire to educate young women as holistically as possible. RGS maintains a secular perspective, based on excellence in and for society. Since MGS is a Methodist institution, a certain degree of Christian education tends to seep in. As with ACS, there are actually two intertwined traditions of material as well as spiritual excellence. (I call it 'missionaries and merchants' for fun.)
Because of these somewhat different backgrounds, perhaps, RGS girls tend to do things as individuals more than as parts of a group or network, compared to MGS girls. As society as a whole gets more socially networked, this slight tendency should make less of a difference.
Similarly, you can find snobs in any elite school. It is often a function of the families they grew up in. However, snobbery is also a function of income disparity and the way children are brought up to view it. It is most intense when income disparity is less, surprisingly, because then the need to discriminate between 'high class' and 'low class' becomes greater. That is why in some societies upper middle-class people will find ways to distinguish themselves from not-so-upper middle-class people.
But there are many forms of snobbery — class snobbery, wealth snobbery, academic snobbery, and even 'what football team do you support' snobbery. Sometimes, snobbery is something young people grow away from.
To answer the question: neither school provides greater holistic education, but they certainly try to provide one.
To answer the allegation of excellence at all costs: RGS girls do excel, and it would be silly to tell them they are not expected to — but not at all costs; MGS girls excel too — they have been a top-10 school for many years, often doing better than ACS(I).
To answer the allegation of snobbery: perhaps a few MGS girls can be seen as snobbish, but this is true of some people in any situation where social networks are an important part of the story; RGS girls do come across sometimes as valuing their own opinions rather highly — but that's true of many gifted and talented people.
How's that?