When I moved from Ossining NY to Princeton NJ I didn't notice much change in my utility (gas and electric) bill. This was a bit of a pleasant surprise as my new townhouse is considerably bigger and is also an end unit with much more exterior wall exposure (compared to the middle unit I had in Ossining). I had some vague thoughts that perhaps my new unit was better insulated or had more efficient heating and cooling systems but upon investigation it appears the main reason is that utility rates are much lower in Princeton than in Ossining.
In 2012 I paid PSEG (my Princeton gas and electric utility) $998 for 890 Ccf of natural gas while in 2011 I paid ConEd (my Ossining utility) $1090 for 562 Ccf. So my average rate dropped from $1.94 per Ccf to $1.12 per Ccf. Similarly my PSEG electric bill in 2012 was $947 for 5193 kWh while in 2011 ConEd charged me $890 for 3451 kWh. So my average rate dropped from $.258 per kWh to $.182 per kWh.
I was aware that New York utility rates are high compared to the national average but the difference with New Jersey is more than I expected. For context the national average natural gas rate seems to be about $1.10 per Ccf and the national average electric rate is about $.12 per kWh (in both cases for residential users).