Part 1: Equipment
To put it bluntly, a lot of people came back with the introduction of the 2007 servers. Some of them might find their way into an EoC server, at which point they'll discover that, while the tutorial covers the new content at a basic level, there's very little information about things that only changed. The thing is, a lot of the changes are less daunting than they seem, they just take some getting used to.
Possibly the greatest change is in equipment, thanks to a combination of class and tier systems. Long story short, defense and the combat triangle actually matter now, and all armor works like magic armor used to: you take a pretty big hit to accuracy if your weapon's class doesn't match your armor's class, 17% if your weapon is strong against your armor's class (for example, melee armor and a ranged weapon) and around 30% if your weapon is weak against your armor's class (melee armor and a magic weapon).
The tier system is slightly more intuitive. Stats are now tied much more closely to requirements: level 70 weapons essentially have the same accuracy and similar damage, and they're better than level 60 weapons. Two-handed weapons have higher damage while one handed weapons have lower damage. However, one handed weapons can be paired with an offhand version of another weapon from the tier to increase damage, or they can be paired with a shield to increase defense prowess. As a whole, two-handed weapons staffs are more accessible. If you're level 70-80, you should probably look toward barrows or GWD weapons for melee, the staff of light or polypore staff for magic; and the dwarven handcannon, or chaotics if dungeoneering is an option, for ranged.
The changes to armor are less dramatic, and mostly centered around giving items the same defense stats and health boosts within the same tier. For example, all level 70 chest armor has 429 defense and 1680 life points, though their effectiveness is different depending on class: magic armor gets its full effectiveness versus melee, 5/8 against magic, and 5/16 against ranged. Some sets have different requirements now: GWD armor is now in the level 70 tier and different from barrows in that it has a small damage bonus. Some of the old classics have had their tiers changed. An example of this would be black dragonhide armor that is now tier 60. Perhaps the most major change is that only a handful of armor items have offensive bonuses: GWD and Nex sets, the slayer helm, and void equipment being the main ones.
How do these changes affect some of the standard items of the past? On one hand, weapons like the dragon dagger or dragon claws are now much less useful for higher-level players because of the removal of their special attacks (though claws can be upgraded at Daemonheim), and items like the fighter torso no longer have offensive bonuses. Defenders and prayer books, the original offensive offhands, are now nearly useless compared to most other offensive and defensive offhand options. On the other hand, almost every weapon is viable within its tier—mid to high level players in particular will find that items like the crystal bow and Zamorakian spear are considerably more useful than they were in the past.
The changes to equipment are probably one of the harder parts of the new combat system to adapt to. If this guide made sense, then it only gets easier from here. If it doesn't, post about it in the Times thread, and I'll try to do a better job with the second part. Alternatively, ask someone for help on the forums or in-game.