The best replacement for atmega328 is atmega328p.

The best alternatives to atmega328 are rated as following:
★★★★★  atmega328p
★★★★★  atmega168
★★★★★  atmega2560
★★★★  atmega32u4
★★★★  atmega32
★★★★  msp430
★★★  atmega16u2
★★★  atmega8
★★★  atmega128
★★  attiny85
★★  8051
★★  atmega16
★  atmega644
★  atmega324
  atmega1280

Your alternative for atmega328 is not listed? Suggest!
Speaking about atmega328, one probably shouldn't forget about arduino uno.

Other search terms related to atmega328 and their ratings are:
★★★★★ arduino uno
★★★ usbasp
You have in mind a companion for atmega328 and it is not yet here? Propose!



Google Trends

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atmega328
atmega328p
atmega168