A few people like crossovers, most don't. You can always get one very cheap that you can put inline between your source and amp later if you want one and there isn't one in your amp (if you can't find anyone to make you one, I'll do it for you for cost of parts + shipping).
The CMoy is a very basic design - it's almost just signal going into an opamp going to your headphones.
The MINT is actually pretty close to being a modified CMoy - it adds a buffered output, which supplies more current to the phones and gives a fuller sound, especially in the bass region.
The PPA is more advanced and adds a "ground channel," which improves response and detail - the ground channel draws the ground current and keeps the output stage from having to push it. This amp also has the most possible options for upgrading components and altering the circuit.
The PIMETA is, to some extent, a simplified version of the PPA, retaining the ground channel but losing many of the configuration options.
The PPA is the best of these in an absolute sense, but is not really portable - you can get one that runs on batteries, but the standard is 12 NiMH AA's - a portable PPA is more like "luggable" and is huge.
The PIMETA is the best of the options that are really possible in a portable configuration. The MINT is fairly simple and can be made much smaller than the PIMETA - small enough to fit in a mint tin. The CMoy is simpler still.
The most popular portable commercial amps are probably Ray Samuels' SR-71 and Xin's designs - his newest (and probably the best) is the Supermono. You could also look at the Meier audio Porta-Corda and the Headroom amps. There are too many to really talk about here - look around in the forums for reviews.