I didn't mean to loose the focus of my original question. These are certainly good choices and exactly the choice I'm determined to make. However, to steal the phrase,
the nutritional thingy, is a nightmare.
There appeared to be a contradiction or I'd missed something in the
blog I'd read. On the one hand, on a low-carb diet the advice is that if
you "ditch the carbs, you should up another macro-nutrient to compensate." On the other hand, the good fats are being lost through draining the oils, but oil was recommended over brine. I was equally questioning whether I was missing something by using tuna in brine instead of oil and is there an important factor for having oil or avoiding brine.
What I omitted (for simplicity) was that whilst my preference would be to keep at least most of the oils (though there is the question about the type of oils and, as others have mentioned, the quality of the oil), draining the tuna depends on the preparation and desired outcome/consistency of the meal. Further to this the preference of other whom you are sharing the meal with; my wife does like the water/oils and is only coming over to the idea of trying different fish dishes.
Apologises for the confusion