Mexican Orange Blossom (Choisya Ternata) - as the name suggests - it originates in South America, so it's not the hardiest of shrubs for the UK climate. I'm not sure what the winter weather is like in Colchester, but the BIG enemies of this shrub are the cold - especially in a windy location. So if you plan to plant it in a shady spot that's exposed to wind, and your winter temperatures fall below -3oC then you may have difficulties. I'm not sure how vigorous it is, but as a rule of thumb any plant grown out of it's natural environment (especially if it's new lodgings are in a colder & harsher climate) is seldom as vigorous or as successful as if it was grown on 'home' ground! Nice as Colchester is, I don't think it can compete with Mexico! A hell of a nice plant though, and fragrant. Beware of snail attack - apparently they often munch on the bark, which is quite unusual, and can cause problems by 'ring barking' plants they attack. It's not fussy about it's soil type (or pH levels - within reason of course), however on the positive side it is very drought resistant (as you'd expect from a Mexican plant - they grow cactuses there don't they?!)
Limelight Elaeagnus is tougher cookie. It is quite a fast growing shrub at approx 30-45cm a year, in the right conditions, and should be trimmed to shape in spring. Unlike the Choisya Ternata this is a very tough plant, it is fully hardy and will tolerate dry soil, growing in full sun or partial shade and is happy in seaside gardens and exposed sites. It won't jib at the cold - unlike the Mexican Orange Blossom. However it only flowers in the autumn. It has beautifully fragrant creamy white flowers in autumn, and it needs to be planted in winter. In fact it is more of a hedging plant often selected in salt air environments that other hedges find difficult to survive in.
The two choices you have made are not really 'like for like' it is more like comparing apples with oranges! The Mexican Orange Blossom will require more TLC, will be quite delicate and not as fast growing. The Limelight Elaeagnus on the other hand is built for our harshest winters and is really a hedging plant - where you plant a row of it to make a hedge. The MOB is more of a 'stand-alone' plant. Now, to hide a big outdoor gas tank, I would advise looking at a climber (Clematis or Honeysuckle), or even something like a Virginia Creeper, that would cover the eyesore in quick time.
I hope that helps!