There are a number of different aspects when it comes to comparing these battlefields, so it'll be best to compare them regarding these aspects.
1) Strategy and tactics of the battlefields: In Crystalline Caves, players have to work out a way to benefit everyone persenally and benefit the team in general. Some people have to be fighters and some have to be gatherers, people who are the strongest (both effect wise, item wise and mount wise) tend to be figters and people who are relatively weak tend to be gatherers who gather and score for the team. Should the fighters not be able to overpower the enemy, they simply fight a fight of attrition and stall them as long as possible. In Battle in Caves, year 386 it's a little bit different. Since everyone is the same level and nobody can bring their things from outside, everyone is pretty much equal, the only difference is their knowledge of fighting and the item sets they choose.
In short, people who fight in Crystalline Caves have to either get their backpack as empty as possible to gather crystals or as filled with wraiths (it varies for different levels, for example level 4 players have to get kakurt & tiger wraiths) as possible to be able to put up a fight or keep the strong enemy players busy, communicate very well and send help to required places or tell their gatherers to run away to base and drop whereas in Battle in Caves, year 386 it's pretty much a fight until you win and gather crystals to score points. It's everyone's duty to do both at some point.
2)Ability to do the battlefield: Crystalline Caves is a battlefield everyone can do at any given time. Players can queue up and be called to the battlefield when both teams reach required amount of players. Battle in Caves, year 386 is different because the max amount one can do this battlefield is decided by how many prayerful calls the player has (maximum 5).
3)Valor, Scalps and Glory: In Crystalline Caves, all of the three are possible receive upon killing enemies and finishing the fights, either by winning or losing since they happen in today's Faeo. As the concept of the battlefield suggests, in Battles in Caves, year 386, it's not possible to receive them during the course of the battlefield. Neither are those handed over to the players after the battlefield since... well, everything the players do stay in the past, they don't reach today. The only exception is doing the missions and challenges of the firstborn, should players complete them, they will receive scalps and other rewards. Last, but not least, players receive a fixed amount of glory & valor when the battlefield is over.
4) Team size: Crystalline Caves requires 9 people in each side whereas Battle in Caves, year 386 requires 6 people on each side.
5) The Bomb: In Crystalline Caves, this feature doesn't exist, in Battle in Caves, year 386 there's a bomb in the middle that spawns every 5 minutes, one should pick it up, go to enemy base and set it off to score points.
6) The Reputations: Crystalline Caves is not the goal, it's just a tool to receive Underground Knights reputation. For example, doing the Dirty Hands recurring quest, handing in crystals and receiving Crystalline Coal then handing them in to the Keeper, finishing Agudar's Feats inside... doing the quests received from the Keeper who resides in Hell's Pass/Foothills is a few of the ways of receiving Underground Knights reputations whereas the in Battle in Caves, year 386 the only thing the players have to do is to win the battlefield and get 5 Reputation of Arbiters of Fate. If they have Mark of The Arbiters of Fate, they will receive extra valor, sacrificial coins and reputation of Arbiters of Fate. Therefore making the whole battlefield the main goal, not the tool.
That's all there is to say about the differences of these two battlefields.