Well, if you want to know more specifics of how PowerVR work read my article here:
http://www.powervr.org.uk/newsitepowervr.htm
Or the official one here:
http://www.pvrdev.com/pub/PC/doc/h/PowerVR Tile based rendering.htm
But I'll summarise....
Tile based renderers store the whole scene to be rendered before rendering it. This is called scene capturing. The advantages start here, when you have all the polygons in the scene transformed and ready to rasterise then some extra things can be done to them. For example the translucent objects can be sorted in hardware - this is impossible on an IMR. Also, generalised modifier volumes can manipulate objects in the scene. The most effective use being shadow volumes - the only performance hit incured being the transformation of the moifier volumes geometry. Both of these features were left out of the KYRO due to lack of developer interest (gits), they were in the Neon250 (and hence dreamcast) though.
There is the issue of the memory required to store this scene buffer - I can assure you it is a non issue. As soon as you turn 4xFSAA on in a high resolution (such as 1280x1024) your z-buffer increases to 20MB Also, your upsampled framebuffer is also 20MB. This is without multiple buffering. On the KYRO the scene bufer has a
fixed size of 6MB and can almost render enough polys for the 3Dmark 2k1 high polygon test (the scene manager allows it to render properly). It is also not accessed as frequently as an IMR's frame or z-buffer. Also, we live in day and age of 128/256mb graphis cards - even if the scene buffer is 30MB big wow.
Once you get to rasterisation hidden surface removal can take place. This is pixel perfect and no IMR can claim the same. 100% of the pixels PowerVR renders are visible in the final image 100% of the time. It is also a pipelined operation with buffering, so it will never stall the rendering (especially as it calculates 32 pixels hsr per clock). Also as each pixel is shaded (in much the same way an IMR does) values are written to the tile buffer, not the framebuffer. Multi-pass effects that write multiple times to the framebuffer such as lot of transparencies, many texture layers etc..are only written once on PowerVR as the multiple reads/reads are done in on chip cache.
Assuming a scene with 4x overdraw.. (compared to an IMR without saving techniques)
Powervr will reduce the texture bandwidth requirements to 25% of what it was.
PVR will also reduce the number of pixel shader operations down to 25% (on average)
PVR will also reduce framebuffer bandwidth by 25% or more if there is transparency in the game.
Also, one of the not very often touted benifits of PVR tech is that not only is less bandwidth used, but when PVR does use its external memory it can use it much more efficiently. It never writes to the framebuffer in a non-contiguous manner. The only time it reads erraticly is when doing texture access. I have no idea what prefect scheme PVR implimentations use but being as the textures for a particular tile can be known long before it is rendered then I'd say prefetching of textures for each tile into cache would be pretty easy.
The main reason TBR's never took off (PVR in paticular) was compatiability issues (which now no longer exist since the KYRO)and te *cough* time to market of many of their products *COUGH*
If at some point IMGTEC were to release a PowerVR implimentation that was feature complete and actually faster than other cards on the market then they could do really, really well.
Oh yes, did I forget to mention that by using multi-sampling AA'ing (like NV's quincunx but without the ghey filter) can be done with virtually no performance cost on a Tiler. 4x MSAA increases your frame and z-buffer access requirements 4x, but if those buffers are on chip like in PowerVR you total extra bandwidth cost is.....zilch.