Equipment-based supers have an edge over power users in that their powers are able to be customized to fit the situation, upgraded in spare time, and disassembled for parts in a pinch. Gadget users also tend to have a plethora of life skills such as mechanical/electrical engineering, jury-rigging, and computing, all of which can double as a great excuse for a cover identity. However, gadgets need to be maintained, require materials to work with, need to be on your person to be effective, and (possibly the worst con) any item that you have with you could potentially be used by your nemesis should they get a hold of it. Tony Stark has had all of these, the last disturbingly often, happen to him.
Power using capes have the advantage in that their powers are always available, require little to no preparation, and are often limited only by what their user can handle. They also tend to perform better in situations that go beyond the scope of conventional sciences, such as magic, alien encounters, or alternate dimensions, as they are already used to working in paranormal conditions. Some of them may have even gotten their powers through a situation similar to the one now causing trouble for them. Downsides of having powers include narrow-scope application, a poor understanding of how your powers actually work, and the troubles that come with power sets that counter your own.
Gadgets can be a great aide to power users as well as gadget users, since if you plan properly, you can always have the right tool for the job. Where they can hinder is if they fail, don't work as intended, or have side effects that necessitate shutting down other powers. For example when going up against a stronger super, it makes sense to bring a device that disrupts powers. However, you will also be working as a mundane while the device is active.
The main weakness of using gadgets is that they're not always there when you need them. Half of any video game is reclaiming/upgrading tools. Powers don't get left behind in the spare Batsuit.
However gadgets an overlooked advantage over powers - consistency. Often, powers wax and wane with the hero. On the other hand, a well built freeze ray will deliver the same power and range with each blast. Yes, gadgets do require practice and maintenance, but so do powers. Superman wrecked the family tractor and Johnny of the Fantastic Four has absentmindedly set some paperwear on fire. On the con-side, gadgets fail when pushed. It doesn't matter how dire your need is, a 250lb wire will not carry 250.1lbs. Powers limits can often be surpassed. A gadget is static.
A good example of gadgets helping a heroes is Spider-Man. The original Stan Lee character doesn't make webs from his wrists. So he invents webs-shooter and the webbing formula. His mobility and combat potential are easily doubled. Powers and gadgets aren't exclusive. Gadgets hinder if the hero sacrifices his/her natural adaptability for single features. Any person who's designed armor can relate to this. Bullet-proof armor restricts torso mobility. However, too little protection leaves countless organs exposed. Gadgets require both creative and critical thinking.
The powered hero, on the surface, has an advantage over the gadgeteer. A lifetime with a power set gives that hero a chance to learn its limits, special trick, and weakness. The gadget based Hero, or villain, is often limited to the design intent of the equipment. A Freeze Ray is a Freeze Ray, no matter how many times it is used. Trying to make it a ice cube maker for a party, or a snow gun for a terminal child's chance to make a snowman in a hospital, would likely destroy the ray gun.
What people often forget is that the right gadget load-out makes the difference on the battlefield. I will now reference the story of Calvin Stingle, a former 'D' list villain. An engineer by profession, he ended up falling into a life of crime. He built himself an powered armor suit. It worked, he pulled jobs, he even gained some credibility with other villains. But until he adjusted his approach to equipping and arming his suit, he was little more than a henchman for bigger names in the business. When he took the time to rethink his load-out, shifting from a rounded out, multiple function suit to a dedicated weapons platform of a walking tank, he became a force to be reckoned with.
The simple example of the gadget user is a person with a handgun, a grenade launcher, and a smoke bomb. Something for small jobs, something for big jobs, and something for when a job goes wrong. A more thoughtful gadgeteer will also have a back-up gun, a stun baton, and a variety of ammunition for the grenade launcher. Only a small difference in his load-out, but one that grants him a much wider set of options for dealing with any given situation. The Powered Hero, or Villain could only wish they were as adaptable.
Gadgets can make or break a hero. It can make a Batman, or it can just as well give powers to someone who doesn't deserve it (i.e. Booster Gold). It can save a life (Iron Man), and destroy them (Any gadget-using villain). By being a gadget-based hero, one can outfit other heroes, and have an ever-evolving set of abilities. However, the start of one's career will be much, much more harder due to constraints of tools, supplies, time and knowledge. And, once again, without any gadgets, there is little that can be done by the gadget-based hero, compared to the powers-based hero. So there are weaknesses that power-based heroes do not have. However, the mind of most gadget-based heroes are sharper than the power-based heroes, as they are contending with forces that are usually outside the scope of their powers, thus requiring inventive and effective solutions, something they share with smart, albeit 'weaker' (See Taylor Hebert aka Skitter aka Weaver aka Khepri) power-based heroes. This means that gadget-based heroes usually rely on their wits rather than their might alone, which is a rather good thing to be honest.