It's common for your old supplier to offer a better deal to try and stop you from switching. Before accepting, ensure it's as good as they say by asking the following questions:
Check your old supplier's unit rates and standing charge are cheaper than ours, as some suppliers may reduce your monthly Direct Debit without reducing the actual price of your energy. This could result in you building up a substantial debit with them.
Your old supplier might also divert your attention from unit rates to the standing charge, especially if theirs is cheaper than ours. But please bear in mind that standing charges have a much smaller impact on your energy cost than the unit rates.
Not only will this show unit rates and standing charge, but you'll be able to see what annual usage estimate they've calculated savings on.
We use the estimate you gave us, or Ofgem's Low, Medium, High values (as indicated by you). Your old supplier's usage estimate might be different, meaning your payments might not be enough for your usage.