I prefer round core bass strings because of the better tone.
https://www.stringjoy.com/round-core-gu ... r-strings/

It's important to know what gauges are on your instrument now so that you can judge what gauges to buy next depending on whether they feel too tight or too loose. Do you know the gauges? If not Kevin will be able to tell you what was used on your instrument.
I can't help much unless i know your current gauges and how each string feels to you.

From calculating the tensions of Stick set gauges i can see that SE has discovered how important it is for tension to fall from low to high strings. This is my conclusion too after many years of adjusting tensions by trial and error on my basses set up for tapping.
I've noticed that a few of the other tap guitar manufacturers have, or had, string sets that do not do this and are similar to conventional bass and guitar string sets.

I found that higher strings are more difficult to get a good response from because they require a tap with more velocity. Thinking about how a tap creates a vibration, it seems to me that the velocity that the string hits the fret needs to be similar to the vibrational speed of the string. So less tension on the higher strings helps because there is less resistance to the tap.

The really tight high stirngs on a normal bass are really difficult to tap as they resist so much and you end up having to really smash the string with your finger.

Lower strings are more massive, have more momentum so they inherently need more tension to keep the vibration 'tight' and under control, with good tone and no floppiness.
So the minimum practical tension of a bass B is around 25-30lbs, whereas a thin guitar string like .009 functions fine as only 10lbs tension, and 30lbs tension would snap it.

So because a tap guitar is a full range instrument, tension has to fall from low to high. The only reason this doesn't happen on basses and guitars is because they have limited range.

Personally i like tension to start at 25-30lbs for very low bass strings, and fall to 10-15lbs for the thinnest plain steel strings. But this will differ for different players.

D'Addario and Kalium both have good tension calculators that can be used to approximate the tensions of any brand of roundwound string.
Once you know your gauges use a calculator to find out the per-string tensions, then you will get an idea of what per-string tensions you prefer.

I noticed the difference in necessary velocity right away. It didn’t surprise me. The way I modelled it in my head is that to create sound, the vibrating string needs to push air molecules around. The air density is roughly constant not matter which string is vibrating, so to produce a sound of a given volume, the strings need to have the same energy.

However, the thinner string has less mass. Therefore, it needs to have a higher amplitude, i.e., it has to travel further for each “wave” to impart the same energy to the air. I theorize there is a similar mechanism at work to get constant sustain.

When I first picked the instrument up, this drove me crazy. So I cheated and bought a compressor pedal for each side. That helped a lot, because I can equalize the volumes between the sides using the volume on my mixer, but between strings on the same side, My technique was ragged.

I’ve recently weaned myself off the compressors. It’s slow going, but I’m getting better at compensating with my technique.

Tapping, compared to plucking or picking, does cause thinner strings to be quieter. I deal with this not with a compressor but by tilting the pickups to bias them towards the thinner strings.