In my experience bigger fish tend to act as you said. They are strong and not given to mad bursts of energy, simply a dogged pull often unstopable. They may want a barny when they get near the net though. Carp are like that, big Trout, Barbel sometimes and Pike usually. No need for them to dash around, just use their weight/power.
Also the power of your rod plays a big part in all of this. For example a 2lb trout on a skinny brook rod is going to be a handfull.
If you feel a big fish on the other end be gentle...it may take some time but be gentle. Try to tire him out long before the net is picked up else it will be gloves off when he sees you. That usually results in a loss!
A notable exception is Salmon who want a barny from the off. Same plan though, try not to get to involved in a war if poss.
Good luck