FPGA or Microcontroller for Production Design?
If you are about equally at home with an FPGA or a microcontroller for development purposes, a microcontroller will cost less in small quantities. 

The lowest cost FPGA listed at DIGIKEY in 1,000 quantity is $US2.85/1000.
 Digikey have a microcontroller part which would do this task for about $US0.30. This is an "outlier" and you would usually expect to pay $US0.50 - $1.00  in 1000 quantity. For $US0.68/1000 you get this ST offering - STM8S103xx  with UART, SPI, IIC, 5 x 10 bit ADC, multiple timers and 28 I/O lines.  

When it comes to doing "bits and pieces" around your core design a microcontroller is going to be substantially more flexible and take less time, unless you are an FPGA guru.

Assembly wise both FPGA and microcontroller are similar.  In most cases you will need external driver ICs or discrete components to drive higher current loads - which probably includes your 7 segment display if it is LED (and not if it is LCD).