I would use a bidirectional blastn program for this. You can predict ORFs and use blastx/blastp if looking at gene content (which might be easier for setting useful e-value cutoffs) or just use blastn. Long contigs will almost always tend to have hits with blastn though.

I have used proteinortho for this quite a lot in the past (at least at gene level). It creates a nice summary table.

Why don't you run a dotlet like program like those that are now being used for comparing a genome with an optical map ? I am refering to DAGChainer. Get the idea from this paper

CD-HIT should be worth a try. CD-HIT is able to cluster sequences quite fast based on user-defined similarity thresholds. Contigs not assigned to clusters should be unique to the respective assembly.

Have you tried Assemblytics? You can use Mummer to align your two assemblies and then use Assemblytics to see the differences.