So I've been seeing a lot of people wear power gloves and tank boots. Is this the best way to wear armor? I'm currently still wearing barrows gloves and cheap power boots such as demon slayer boots and skeletal boots. Should I change my gear?

I wouldn't really say its the way to go as such

It's just a by product of people having glacor boots from pre-eoc and having no desire to chance them out.

As well as being a product of people chasing the highest level gear they can Glacor boots being lvl 85 def and non-degrading vs lvl 80 nex boots which degrade.

I'd say go for the highest tier you can afford without breaking the bank, i.e., if you can afford it, go for Armadyl Boots and gloves. I presume people use that setup because the power gloves are cheaper than the boots, or they just held on to them as Sy said.

As everyone has mentioned so far, it's a money thing. People had Glacor boots, EoC came around, boots dropped in price, and no one is willing to swap them out for more expensive boots. If you can afford it, go full Power armor like GWD armor or, eventually, Nex armor. If you want defence, go with full Superior PoP armor. Then you just have to buy Glacor boots and Automaton gloves. :P

Let us not focus simply on boots.

Think about if there are more efficient upgrades. I mean skeletal->glacor means a 72 increase in armour and a drop of 10.5 in ability damage, at the cost of 9m+

If something else gives a bigger boost(eg batwing->subjugation) why not do that first? Gloves and boots are usually left for last.