Strut bar vs suspension upgrade?

there are many options available to improve handling.

a strut bar is a chassis re-enforcement. it keeps the car from flexing around where it shouldn't (suspension movement is good because you can control it, chassis flex is not good because you can't control it)

lowering springs lower the ride height for your car giving you a lower center of gravity and stiffer ride. a stiffer ride means less roll in corners and better turning grip (by staying balanced over the 4 wheels you get the best grip possible)

coilovers replace your regular shock absorbers to give you more settings. a good adjustable kit will let you lower the ride height to a desired level, as well as change the damping settings (how much the car bounces after a bump or weight transfer) and ultimately a bit of the stiffness.

an anti roll bar is a bar that attaches to the chassis and suspension to keep the car from rolling in corners. up and down travel on both wheels like bumps will not be affected, nor will the ride height or stiffness.

lastly there are tire upgrades. better performance tires offer higher levels of grip allowing you to corner harder. they do not affect the ride height (unless you get different sized wheels and tires). they can somewhat affect ride stiffness depending on their profile. tires act as a spring. low profile tires are not springy and will let you feel more bumps in the road. generally, low profile tires only benefit looks and in some cases the ability to fit large brakes on the car. if you can already fit good brakes in your regular wheels and are happy with the looks, high profile tires (thicker) will absorb tiny bumps in the road better and will give you a smoother ride. (formula 1, rally and nascar use high profile tires)

I don't mention aerodynamics upgrades because at road speeds aerodynamic parts serve no purpose other than adding weight and drag.

now to decide what would be best for you.

turning performance/agility is based on weight and weight transfer. the lower the weight the less inertia when you turn.

now the most easily controllable aspect is weight transfer. because of inertia, when you turn your car rolls. roll is bad. when your car rolls, you spread your weight unevenly giving the wheels with less weight on them less grip. by keeping a car flat in corners you provide each wheel with the most grip possible. cars with specialized aerodynamic parts like formula 1 also work better when they are flat, not rolling. unfortunately, cars also need to be able to handle bumps. this is the problem that suspensions create. they can make a ride very comfortable by being very soft but at the same time they make the car handle poorly. this is why it's good to isolate effects. by being able to work on individual effects you can fine tune your car very well. if you want better cornering with still a good ride comfort an anti roll bar is the best upgrade. anti roll bars retain your suspensions ability to absorb bumps while keeping the car flat during cornering. they are also relatively cheap and somewhat easy to install. keep in mind a low quality anti roll bar will flex a lot and not really do much. with a strong anti roll bar you can drastically reduce roll.

lowering springs/stiffer springs and coilovers/stiffer shocks can reduce body roll but they also affect ride quality.

lastly, you could always change the steering system for a faster system. this means you would have to turn your wheel less to get the same amount of turning. these can be very expensive and dont improve the traction you already have. this is only typically done on dedicated drift cars that need to be able steer a lot in either direction to maintain control while sliding around at high angles. (racecars sometime get their systems changed for better driver feedback and lower weight)

Replace all your Rubber bushings with URETHANE. A thicker sway bar and stiffer shocks will also stiffen it up....that's what car makers do on sport models.

Great answer Geo