What's more important is somewhat of a subjective topic. The concept of duality is one way to frame it: every electrical thing has a dual. One of the more obvious examples: Capacitors are the dual of inductors. Everything that's true about inductors (ideal ones, at least) is also true of capacitors, if you exchange voltage and current, series and parallel.
There are also many electrical machines that have duals. For example, the common loudspeaker is driven by magnetic attraction or repulsion between an electromagnet (voice coil) and a permanent magnet. These are low impedance speakers (usually \$4\Omega\$ or \$8\Omega\$, meaning that an amplifier designed to drive them will be designed to output a large current over a small voltage. But, there are also electrostatic speakers which are high-impedance devices (\$>10M\Omega\$, easily), driven with small currents at high voltages. Rather than being a mostly inductive load, they are a mostly capacitive load.
The world is full of these duals. So as far as theory goes, mostly voltage and current can be exchanged and you end up with a different circuit or machine that accomplishes the same thing.
However, we live in a biased world. Voltage sources are more common than current sources. When we represent physical quantities electrically (like sound pressure) we tend to analyse them as voltages, not currents. When we think of a mechanical actuators, we think of magnetic solenoids before we think of electrostatic ones. I'm not entirely sure why this is true, but it is. Maybe it has to do with the practicalities of constructing things with the materials we know about. I've actually thought about framing it as a question on this site, but I couldn't think of a way to do it that wasn't too subjective.
Here's the lesson to take away: because voltage sources are so common, it's common to only need to consider the current, because the voltage has already been decided for you. If you have say, an Arduino that runs from a 5V supply, then you don't think about the voltage. The voltage is 5V, and there's nothing you can do about that, if you want to use that Arduino. All you can change in your design is how much current you require that 5V supply to provide.
However, there is no theoretical difference in importance between current and voltage. They are two sides of the electrical coin, equally important. And, in many cases, you can trade one for another. Consider both equally in your thinking.