Why haven't modern grass based crops overrun wild grasses?
Modern grass crops (cereals) haven't run out in the wild is because that was the whole purpose of their development. What differs them from their wild counterparts are the domestication traits, like, seed shattering, uniform maturity, day length sensitivity etc.


  Modern grass based crops are significantly superior to wild grasses, they grow faster, are stronger stemmed, have larger leaves and higher seed yields in terms of individual seed size, giving germinating seeds a significant head start vs other wild breeds.


This is only true under well resourced conditions, such as, irrigation, fertilizer, planned planting density etc. They grow faster and stronger because that is how they are bred. They are bred to utilize these resources better and produce better.


  I've heard time and again that GM crops will escape into the wild with potentially devastating consequences, out-competing wild plants for space and destroying biodiversity.


What people generally talk about here is the genetic transfer due to pollen contamination. But this is generally hard because of species differentiation. Even if that happens it will be with very low frequency compared to wild population. As far as I know modern crops do not and probably will not out compete wild plants under natural conditions.


  So why hasn't this happened already? Our crops are already GM (albeit through different methods and over a much longer time)


Explanation above applies here too.


  Edit: I have seen the odd crop plant growing in the wild, amongst other grasses, but rarely more than one or two clumps of wheat or barely grass amongst a sea of wild grasses.


That is generally due to seed contamination due to somebody threw a seed there. Or it is due to remnant seed from previous year's crop, these plants we call volunteer plants.