Mitchaa,
I no longer work in Nigeria, but presume you would be going there to work for Bristow. If you do, you'll have free medical insurance (and can pay an additional fee to have your family included), and the same type of pension scheme as in UK (you can pay in up to 7% of your salary and Bristow will match that).
If you're on equal time and you spend your time off, you'll be liable to UK tax. You can only spend a maximum of 90 days a year in UK if you want to be tax free (and your days of arrival in, and departure from, the country count as days in UK). You could do as some others have and either buy or rent in most other European countries where they have a more kindly tax regime, the majority allowing you to spend 183 days a year in country. This is not practicable for many people with children who don't want them to up sticks and school outside UK. If you work for Bristow they'll pay your 20% tax for you. However, the Inland Revenue class this as a benefit, so in UK you'll be taxed on your salary, plus the tax Bristow pay for you to calculate the total amount of your tax liability. You'll then be given credit for the 20% already paid (as long as you can get your tax certificate). If you work for Caverton (unless they've changed, which I doubt), they won't pay any tax for you in Nigeria, in which case you may also have a liability for unpaid tax in Nigeria if you're caught.
I've worked full-time overseas for many years and spend less than 91 days in UK. However in your case, unless you want to move to another European country, you're probably better off staying where you are, especially if, in addition to working an equal time roster, you're home with your family every night.