What is the advantage of the way eukaryotes initiate translation?
As far as I understand it (and I'll preface this by saying that initiation is not my strongest point), but prokaryotes utilize the beautiful AGGAGG Shine-Dalgarno sequence.  Usually around 8bp upstream of the start codon, it is this sequence that the prokaryotic ribosome seeks out to initiate translation.  It does this through a complementary region in the 3' sequence of the ribosomal RNA.  Upon complementary binding, the ribosome and mRNA are correctly bound.  Convenient!

In eukaryotes, however, there is no consensus SD sequence, so a different mechanism must be used; the complex of 40S and Methionine tRNA serves this purpose.  The two together scan the mRNA, looking for an AUG start codon which the tRNA is complementary to.  This eventually brings the full ribosome (40S + 60S) together to start translation.