The primary benefit is more capacity for less weight. For instance, a 100Ah LiFePO4 battery weighs ~30lbs. You can also safely use almost all of that capacity without prematurely aging the battery. If you were to follow the AGM 'rule of thumb' of only running your batteries down to 50% on a regular basis - that 100Ah LiFePO4 battery has equivalent capacity to 3 of the stock Exide 70 Ah AGM batteries, which would weigh something like 150lbs. So you get the same energy storage at ~ 1/5th the weight and 1/3rd the size.
There are some other minor benefits - the battery voltage is slightly higher (~13V) and doesn't significantly drop as the battery drains, so you are still getting 12.8V near full discharge. The internal resistance is also lower, so you can theoretically charge them faster if you have a high amp alternator. The lifetime is also theoretically longer - 2000 - 4000 charge cycles, although there is some evidence that this doesn't hold up so well under real world conditions. You also don't need to worry about not fully charging the battery between cycles - it is fine to run the battery down to 30% then only charge it back to 80% before running it down again.
Of course there are also drawbacks. They are much more expensive $900 for a plug and play 100Ah solution (Starkpower) or ~$600 for a DIY solution (4 CALB 100Ah cells). You also need to be a little more careful with charging and discharging. While the commercial versions have a built in Battery Monitoring System (BMS) which protects the battery from abuse, you still need to be aware of the slightly different requirements for care and feeding, particularly if you go the DIY route. Finally, what may be the biggest issue for using these batteries in a vehicle/camper - they shouldn't be charged in below freezing temperatures (<32F or 0C). Discharge at low T is fine, but charging could dramatically shorten the life of the battery. If you winter or shoulder season camp, this is something you need to be aware of and address.