I think if you say 'tighter turn' instead of 'faster turn', you might get the answer youre looking for. Im not sure if deploying landing gear or changing pip settings affects these things more than drive mod choice. ie. by using flight mechanics maybe you can have your speed cake and eat it, with better low speed agility & therefore tighter turns (that cover less distance) when you want that, but full benefit of boost speed & max turn rate that drag drives give.
For permaboost ships, drag drives are surely the best option, for more mixed flying styles, maybe its not so clear-cut..
4 pips to Eng will tighten a turn by increasing the force exerted by the translational thrusters that provide both the rotation (via pitch etc) and the thrust. The inputs required to achieve the tightest turn will vary by ship speed and vector, ship type (as ships have different ratios between rotation and translation) etc. But basically in all cases the tightest possible turn will involve both rotation and translation being used simultaneously.
However...
...I feel I have to repeat again that this really doesn't affect the answer to @Draxxa's question, which concerned which engineering to apply. In every single case the answer is the same: 'whatever would give your ship the highest max speed.' That provides the strongest starting point for the tightest turn because, in direct proportion, it also provides the best rotational stats and strongest translation thrusters - at any speed.
In Elite Dangerous, the answer is always the same:
'If you want your ship to be able to manoeuvre more tightly, engineer your ship for maximum top speed.'
(I do repeat, though, again that the exception to the above is regular drives v enhanced drives on small ships. That is a purchase choice, not an outfitting choice, but regular drives provide stronger thrusters, compared to top speed, than enhanced drives.)