OK so now for the promised details. Again, I don't know for 8008 so please correct me - I will refer to 8080.

• 4004 has 16 so called index registers (4-bit), which operate mostly in pairs -> eight 8-bit registers. Sounds familiar? 8080 registers are specialized, not exactly for indexing.
  
• there are indirect RAM operations using the index registers, although in a two-instruction form (first move address from register to a address latch in RAM, then perform the operation). Similar to @Rn instructions.
  
• there is a testable input pin (8048 has the same). Nothing like that on 8080.
  
• conditional jump within a 256-byte page (not displacement). 8048 - the same way.
  
• ROM table fetch (line MOVC in 8051, exactly like MOVP in 8048) within a page.
  
• ISZ - increment index register, skip if zero. Changed to DJNZ in 8048/8051. Nothing like that in 8080.
  
• keyboard decoding instruction (KBP). Although there is nothing similar in 8048/8051 (nor in 8080), this sounds really more like an embedded feature rather than a general-purpose processor instruction.

There might be more subtle differences and/or similarities, of course.

By the time 8048 got designed, of course, both 8008 (8080) and 4004 (4040) was known to the designers. Nut for me, it really sounds that the direct line is 4004->(4040?)->8048->8051, and 8008/8080 is the "uncle" of 8048.

Jan Waclawek