Many a time I've seen someone try to see how Power Armor could be used well, (in combat) they act like tanks on a smaller scale. It got me thinking "If these PA users can take small arms fire, hold incredible amounts of ammo, can operate well in soft ground and non-spacious environments like a forested area, whats stopping a tankette like the german Wiesel series from doing the same thing but faster (wheels/tracks) and being more reliable at the same time?"
Ease of use and training. The PA moves and acts like a human would, which is easy to learn. You can also do many things with it, like trench warfare with much bigger weapons and more dangerous to enemy armor than regular armor (or a wiesel) would. Tanks and tankettes cant do trench warfare as they require a pre-prepared position they have to drive into and out off, being vulnerable in that time where a PA would just pop up and back down again.
PA's are also easier to use in other roles, like digging fortifications, short-range transport ("get that ammo to the other side of the compound quickly and come back!"), loading/unloading, making clearings etc.
Like all questions about mechs versus tanks/wheeled vehicles it should not be about which one is superior, but what roles they can be used at. We dont use exclusively tracks or wheels after all, they each have their specific uses. Legged armor/vehicles would be no different.
The way you describe your power armour, a role that they could perform better than Any other infantry would be that of shock troops. (https://en.wikipedia.org/wiki/Shock_troops) Any well equipped infantry unit tasked with the first assault against fortifications or an enemy position would fall under this description, and troops with equipment like power armour that could withstand small arms fire would be ideal for this. They would be an elite infantry unit used as a "tip of the spear" for their army.
As pointed out in an earlier answer, their main advantage over over vehicles would be their ability to fight well in difficult terrain, especially urban warfare since history and research has shown conventional military and vehicles and tanks to be terrible at this.
(https://www.researchgate.net/publication/348960360_The_Effectiveness_of_Armoured_Vehicles_in_Urban_Warfare_Conditions) this article discusses in detail the most common types of attack performed against vehicles in urban environments in modern warfare, and over 80% of attacks are carried out using smal arms fire. Infantry that could withstand this would be ideal for leading an attack on urban areas. It is an interesting read, it even has a Sun Tzu quote about avoiding urban warfare, even back then they realised that urban warfare is a destructive and costly affair.
Most conflicts in recent history involve urban warfare, and this trend is expected to continue. It is also predicted that by the UN that in 2050 about 68% of the world population will live in cites, natural increasing the chances that conflict will occur there.
hope any of this helps!
Hard to answer without a lot of engineering details and specs for the different systems but in theory traditional 'power armor' as portrayed in SF and as opposed to say 'Mechs' basically just amplify the levels of personal protection, carrying capacity and potentially endurance of an infantry soldier, not to superhuman levels but enough to make a difference. With one proviso.
The universal trend in military history has been that as the weight of the arms, amour and pack that soldiers are expected to carry has decreased over time with improvements in technology commanders have tended to add on extra pieces of 'essential gear' so that the weight goes back up. The result is that your average GI today today is basically expected to carry pretty much the same total weight as a Roman legionary was!
So lets assume your brand spanking new power amour lets a soldier carry twice as much as was previously possible. If so a lot of the expected benefits would be lost if that solder was immediately given twice as much extra weight to carry.
Lets say for example that they decided to take away the power armored GI's M4 carbine and replace it with a SAW. He now packs way more firepower but also loses a lot if not all all the extra agility etc the amour may have otherwise given him/er due to the extra weight of the weapon & ammo they now have to carry. So a lot would depend on the role commanders saw power armor playing on the battlefield e.g. close in assault or long range patrols. You equip the suits differently depending on the mission.
That said your power armor should still be superior to the vehicles you mentioned in close quarter assault rolls and/or in rugged or close terrain like dense forests, mountain sides or inside industrial and urban landscapes. No matter how versatile a light tank may be its not climbing up a spiral staircase, rappelling down a cliff face or weaving its way through densely packed jungle anytime soon! It simply wouldn't be as compact or as flexible as powered armor.
Broad rolling plains or other mostly open spaces? Different story entirely. The vehicles would probably have major advantages in speed and maneuverability and carrying capacity (including long range sensors).
So it would be a case of horses for courses. The objective and terrain your operating in sets the parameters on the type equipment you'll deploy. They might both see wide service, just not always in the same operations.
The tankette is a rather easy target for bazookas, anti-tank-missiles, gunships and drones. It is big, has a large radar and IR signature, and you hear it from a distance.
Once you can put BAs with similar firepower and protection onto the battlefield in large numbers, tankettes don't make sense anymore.
That said, there will be an arms-race between infantry rifle's penetration and the BA's protection, and the BA might as well loose this race: Todays infantry rifles are not optimized for penetration, because they don't need to be, but there is much potential for improvement, like higher muzzle velocity or optimized penetrators.