It won't feel as planted as a newer S4. Those cars are lighter, wider, and designed to be sportier.
For your A4, if you haven't done it, the rear sway bar (either RS4, 034 Motorsport, or Hotchkiss) will really improve handling--it's immediately noticeable as soon as you take a curve. You could definitely upgrade the springs and struts if you want to lower the ride with a firmer feel. On a budget you could go with ST (IIRC, somewhere around $600-$700), otherwise, they price up to $2400 or so for the KW v3 (if you don't want an air setup).
At 90k I recall my control arms feeling ok; I'm almost at 140k now and probably should've replaced them a few thousand miles ago. Do an inspection, and if they look like the ball joints and/or bushings are worn, time to replace. And don't do one side at a time--they should be replaced in pairs. Are your tie rods and wheel bearings good?
Another area to check would be mounts. Improved engine, transmission, and rear differential mounts will give you more direct feedback at the risk a slightly more vibrations. 034 are popular upgrades for those, same with Apikol and now ECS too.
One other consideration is wheel/tire choice. I'm not sure what you run, but going to a wider tire (say, from 235 to 245) will increase handling, as well as what type of tire (all-season vs summer). Wheel-wise, if you lighten each corner with a lighter wheel, you will absolutely improve handling via reduction of unsprung weight. Brakes are another area you can potential save weight in, if you want to go down that rabbit hole.
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