They might be a more elegant weapon for a more civilized age, but lightsabers are not the be-all, end-all weapons of the galaxy. Sure, they're probably the coolest as they're portable and require special individuals to wield, but many other Star Wars combatants have proven that other weapons can do just as fine, sometimes even better.
In fact, there have been a number of weapons used by certain individuals to beat the Jedi. More impressive even is the fact that most of them are not even force users nor possess advanced laser swords that can cut through anything. So it stands within reason that maybe, just maybe— and in better hands, some of these weapons can be more powerful than lightsabers.
Slugthrowers
The reason why lightsabers are so effective against most combatants is that blasters are the most ubiquitous weapons in Star Wars. Lightsaber blades pretty much nullify a blaster's ranged capabilities because they're lasers too. So what happens if the projectiles are solid objects instead of light?
Obi-Wan learned how deadlier those are than blaster fire in one Star Wars comic book. The weapon type is a slugthrower that fires kinetic metal projectiles much like today's guns. Even if a Jedi manages to block the projectile with a lightsaber, some of the projectile's shrapnel will still go through and they also cannot be deflected due to their weight.
Beskar Spear
One of the few things in the galaxy that can withstand lightsabers is Beskar steel. These are precious Mandalorian metals that were used for their armor and some of their weapons. As was shown in The Mandalorian, even a simple weapon like a spear but made out of Beskar can easily best a lightsaber.
It was Din Djarin who wielded the Beskar spear against Moff Gideon who had the Darksaber. In the hands of a more experienced melee fighter, the Beskar spear would have been deadlier and pretty much explains how the Mandalorians were a match for the Jedi.
Electrostaff
Of course, it's not just Mandalorians who were smart enough to employ their own anti-Jedi technology. Separatists also had their own armaments that can withstand lightsabers. General Grievous' retinue, for example, had Magnaguards equipped with electrostaves.
They're not efficient since they're droids but electrostaves can definitely be used to defeat a Jedi user. Other variants include batons and other electric weapon forms. Even Darth Vader himself managed to defeat a Jedi with an electric weapon.
Mounted Blasters
While one of the strengths of lightsabers is that they're incredibly efficient against blaster fire, not all types of blaster fire are of the same strength. Some of them are bigger and more explosive than others such as those from mounted guns or cannons.
Blaster fire from space vessels, for example, are probably too much for the Jedi to handle as some of the projectiles are likely bigger than them. Even clone trooper mounted blasters or cannons will also do it against the regular trained Jedi.
Whistling Birds
Much like slugthrowers, Whistling Birds fire solid projectiles at a target and these cannot be deflected. Mandalorian Whistling Birds are small needle-like target-seeking darts that are made out of pure Beskar. That's also another reason why lightsabers are no match for these.
It's not clear how Beskar vs. lightsaber physics work in Star Wars so whether the Whistling Birds will get deflected or not is up for debate but with how many of them are fired at once, there's no way a Jedi can avoid them all. The downside is that ammunition for this is precious.
Mandalorian Rockets
Another Mandalorian weapon that would probably make lightsabers less desirable on the battlefield are rockets. Most Mandalorians seem to pack at least one rocket attached to their jetpack. Boba Fett did have one and it's reloadable.
As for its effectiveness against lightsabers? Good luck deflecting these no matter how good of a space monk you are. They will explode on contact and maim or kill the target. Force users can, however, seize the rocket before it hits using the force, assuming they're that good.
Flamethrowers
It's pretty clear by now that lightsabers are only best used defensively against small measly blaster fire. Explosive forces and weapons make a lightsaber wielder's life too difficult. Flamethrowers are no exception, they can't be deflected nor stopped at melee range.
A flamethrower can make quick work of any Jedi that relies too much on their blocking abilities. It does seem that the Mandalorian flamethrowers need a bit of a rework since they could use more range; there are modern flamethrowers more powerful than what Mandalorians currently have.
Seismic Charge
Grenades would also probably work just as well since they also can't be deflected and the shrapnel count is too much for a lightsaber to block. However, those can be easily caught and thrown back, especially by lightsaber wielders.
For better damage and surer deaths, the Fett clan's specialty, the Seismic Charge, will work much better. Even if the target manages to catch it midair, it can still detonate and deal extensive damage from afar. Of course, it will also probably kill the thrower due to how powerful it is, but that only proves how much more dangerous it is compared to a lightsaber.
Amban Rifle
Based on what was shown in The Mandalorian, the Amban or disruptor rifle could be a lot more dangerous than a lightsaber. It has two tongs that can electrocute a being as big as a Krayt Dragon but more importantly, it functions as a sniper rifle as well that can vaporize targets as big as a speeder.
Now, it's not explicitly stated whether the Amban rifle fires lasers or slugs but with the way Mando loads the ammunition, the projectiles seem to be special. It may or may not be deflectable by lightsabers but since it's a sniper rifle too, it's safe to say that anyone wielding the Amban rifle against a lightsaber user already has the advantage and element of surprise.
The Force
A lightsaber might be a Jedi's most common weapon, but they wouldn't even be able to make or wield one without the force. It's the force that makes the lightsaber's kyber crystals usable. Besides, there are Jedi and Sith who have relied more on weaponizing the force than melee combat.
People like Count Dooku, Yoda, and Darth Sidious have proven that the force can be an even more powerful weapon than a mere laser sword. Even exiles like Ahsoka Tano were able to deactivate lightsabers using the force so for more advanced force users, the lightsaber might as well be just a fancy graduation token.