But what are the drawbacks of p-Series-type virtualization? What are there things that first type of virtualization can do, but p-Series type of virtualization cannot do?

The only drawback for IBM virtualisation would be if you are running an emormous Oracle database. This LPAR could benefit from dedicated fibre adapters to connect to its own external storage. However the industry standard now is to provide 4 VIO servers per frame. These are further split into one pair providing networks and the other pair providing storage. The use of NPIV (Virtualised Fibre Adapters) also helps with the write and read latency.

I feel you should stop thinking of the AIX environment as a virtualised system along the same lines as a VMWARE system residing on host system. The IBM virtualised system is a large number of seperate AIX machines sharing CPU and memory resources with I/O being supplied via the VIO server.

Also what ZXMAUS has said is quite acceptable but even if you are dealing with a lowly P520 (P720) you would have enough power available to build two VIO servers and a couple of LPARs. One LPAR could provide your running production environment with AIX 5.3 and you apps installed. With the second LPAR having either AIX 6.1 or 7.1 installed as a development system to check the stability of the APP in the newer environment. Neither system would know or interfere with the other!

Hmm... You're saying that I can (in principle) move my app (and its LPAR) from box to box easily. And can I (again, in principle) at all decouple my app and my boxes? I.e. have a bunch of IBM boxes and some "hyper-LPAR" that aggregates all of them into one big machine? And my app that runs on that "hyper-LPAR" and doesn't really care whether it in reality executed on box A, box B, or even both boxes A and B? Do people do that?

Why would you want to? How will it share resources? AIX 6.1 and 7.1 both support "Live LPAR Mobility" which enables an LPAR to be moved to another LPAR in a frame, or between two different frames. There is really no such thing as a "hyper-LPAR". The only thing which would allow what you are describing is HACMP or Veritas Cluster Manager (VCM).