It has all the 328 hardware ... just less memory and it won't work at lower voltages.
The 8L variant works at down to 2.7V. Tradoff is that it is only clockable to 8MHz (but that's OK if you are running them without an external xtal, in which case you would only be doing 8MHz max anyway.) These make nice Attiny substitutes if you need more pins than on an attiny85, for example. I bought about 10 a while back for this reason.
The other limitation no-one has mentioned so far wrt to the newer 168 and 328 is that you can't use all the pins for pin change interrupts. It really just has the INT0 and INT1 external interrupts available (although there are some kludgy workarounds on some of the other pins to simulate pc ints if you aren't concerned about interrupt priority.)
If you can live with 8KB flash and 1K sram then they are certainly a viable option.