Hi,
The Starter kit uses the 20 pin 16F690 chip which cannot directly use the Debugger function - forget about using all the adaptors that are available to make it do so - its not worth it.
However, the picture shows it to be fitted to an ic socket so you could change the chip for something pin compatible.
The Debugger board uses a 44 pin SMD, Surface Mount Device, which is soldered directly to the pcb and cannot be changed.
There is little between them, but my choice would be the debugger board as it does give you that facility to try later on.
On a more practical note, neither board will be much use long term, they are really just to give you a proven working board to start your initial programs on such as the proverbial flashing a led, but for this introduction alone either one is worth it.
Also when you actually get your pcb you will be amazed how small they are, and again you will soon move onto a larger bread board or make your own pcb to work on - but don't think about all that yet as will be more obvious once you have mastered the Starter or Debugger Kit.
good luck