They have had the advantage of success at a peak time in the overall growth of fan numbers. That's the only thing that's bigger.
Historically, there's no way they were a 'bigger club' than OUFC. In the early 80's, they had lower crowds than us. Our successful years were when football was at its lowest peak, pre-Italia 90, pre-Sky and pre-fit for purpose stadia. They benefited from a custodian who took that word seriously and put glory over return. We didn't.
Their away support is very low in numbers. I think that says a great deal about the nature of much of their support. Those they have added over the last 15 years or so are fans of convenience. They buy their tickets, they call themselves fans, but the numbers don't lie - their % of home crowd that travel away is much lower than ours. A sustained period of proper decline and we'll see it melt away. Of course that's a sweeping generalisation, but I don't think it's too far out.
OUFC > RFC.