Transducers generally are money well spent, so speakers and mics are usually the places to spend the money, and a good pro grade speaker can easily be the thick end of 10dB more sensitive then the cheap stuff.
I would note that it may be that some acoustic work on the room might pay off bigtime, and that given you have the height, getting suitable speakers ...
Which components in a sound installation are likely to have the greatest effect on sound quality?
In this order:
The input (ie performer / musician etc..)
Acoustic treatment of the room
By utilizing the crossover, the mains can produce the mid and high frequencies much more efficiently, and thus louder and with less distortion. I cannot imagine an application where this would not be preferred. Using the individual eq on each channel on the mixer should achieve the desired result. For PA or speech, for instance, I dial the bass back, and ...