"Chunky" Graphics are the kind that most people are used to these days - where your graphical data tends to be addressed as pixels where each pixel has a single address and stores all data in one place.
For example, your typical modern RGBA buffer will be composed of linear array of 32bit values, each of them representing 8bit Red, Green, Blue and Alpha values of individual pixels.
Planar graphics works differently, with separately addressed bitplanes for different types of colour. For the RGBA example, you'll end up with 4 different buffers, each buffer representing red, green, blue and alpha values separately, requiring separate writes etc. - however one write in single bitplane could mean multiple pixels affected.
Both approaches have their pros and cons, but in this case we're going to focus on Amiga's downfall-related specifics.
When Amiga's graphic hardware was designed, a lot of it was built with features relevant to then common "home computers", even if much more powerful. This included things like "playfield" and hw sprite support, things especially useful in 2D games. Multiple playfields allowed compositing of two colour-limited screens on top of each other by dividing available bitfields between the two screens. Sprites allowed limited pasting of objects from memory at realtime on the screen (for example, player character, enemies, missiles in a typical platformer or SHMUP game). There was also hw collision detection between sprites.
All of that advanced hw however didn't exactly help with software-rendered even pseudo-3D that became popular around that time - some features could be definitely reused (semi-programmable graphic pipeline through copper, blitter helping with bitmap ops, dual playfield allowing composition of, let's say, cockpit and exterior). Instead, you might want to compose variable-size bitmaps of pre-rendered airplane at different angles (method used by LucasArts 1988-1991 trilogy of WW2 aircraft sims), which didn't nicely match with sprite system, instead considerably taxing the blitter capacity (especially since blitting might have to be done in multiple passes due to planar graphics). Chunky graphics is also generally simpler, but changing requirements from applications definitely had their impact.
More importantly, as someone mentioned, Amiga chips were innovative and powerful... in 1985. In 1986, VGA debuted, and while not particularly powerful on its own or widely available, the increasing power of the CPUs in PCs quickly eclipsed the benefits of dedicated hw chips in Amiga, especially since the OCS (Original Chip Set) only received incremental update in 1990 (ECS) and another in 1992 (AGA). Someone already mentioned writing faster blitters running on CPU than hw blitters of Amiga allowed, plus there were considerable limitations regarding DMA capabilities (IIRC, DMA for graphic system was only allowed from "Chip" Ram, which was limited to 2MB at best? Someone correct me if I'm wrong).
There were also other areas where a dedicated enough PC owner could spend more and build a more powerful machine (wider availability of (E)ISA controllers, 1990's XGA with its higher resolution than AGA and hw blitter, etc. etc.).