Agreed, car allowance and company car BIK are separate.
Car allowance will be set by your employer. Usually on the basis of some kind of salary band or grading system.
BIK is dictated by HMRC as a consequence of whatever company car one chooses.
If you have no cash alternative to the company car, you are taxed on the BIK at the applicable income tax rate.
If you take a cash allowance you pay income tax and NI on it at the applicable rate.
If you have a choice of a cash allowance or a company car, and you choose the car, you will pay tax on the higher figure of the cash allowance or the BIK, unless you choose a company car with emissions of no more than 75g/km.
Which brings me back to my original point. As a company car driver, there is a clear financial benefit to choosing the GTE over the GTi. There is a lot less tax to pay.
If you are a private buyer, the GTE is unlikely to ever save you any money, as the savings in fuel are potentially going to be eaten up by the significantly higher initial outlay. This would be compounded by the GTE also being much closer to the £40k luxury vehicle tax rate, potentially meaning an extra £325 per year in tax if you tick a few options.