This is my article about comparing vacuum tube amps vs SS amps. There are more than enough places that compare there two types from the aspect of sound. I will avoid that and only concentrate on the differences from a DIY aspect.
Solid state amp pros
*Transistors are cheaper than vacuum tubes
*PCBs are available for many amps
*Transistors are usually more reliable and last longer
*power supplies use lower voltages than tube supplies and therefore are much safer. also no need for a separate heater supply
*usually don't need output transformers
*chassis work is typically limited to front and rear panel
Solid state amp cons
*Often necessary to buy a large heatsink
*If no PCB is available, designing and making your own PCB can be cumbersome
*If you don't use a PCB, point-to-point wiring is very difficult
*Need to be careful with electrostatic discharge. Easy to fry a transistor if you aren't...