Is the level of the character going to be persistent or do the game worlds reset and start over from scratch regularly? If persistent, then will a new player be at a massive disadvantage (as in most MMOs) or still be able to hold their own with a more limited skillset and loadout (as in say, PlanetSide2)?
In other words, what role does character progression play in the game?
Yes, it's persistent. No resetting is planned that I know of, and a new level 1 player will not be able to do the things a level 60 player can. However, a level 60 player can't just walk up to you and kill you. If you want to participate in open world PvP, you have to turn on your PvP flag, and you can't do that until you've leveled a bit. As it is now, turning on your PvP flag will mean you get an experience gain bonus, and if you get killed by another player, you don't lose anything except some durability on your gear. The big 50v50 wars are separated from the regular open world, and things even out a little there -- if you're a level 20 character at war and you're facing a level 60 character, they will have a big advantage, but there are 50 players on each side so you're probably just one person trying to hit them. In that context, you could make a difference by getting a few shots in, and when you die you'll respawn and can return to the fight.
Theoretically, since there's a player skill component to the combat, a level 1 character could kill a level 60 character in 1v1 combat. I think that would be extremely unlikely, unless the higher level character had only a sliver of health at the start of the fight. As you level up, you can increase classic RPG stats like strength, agility, and constitution (I don't think they call it that, but it's the same thing). So a level 60 player who, say, focused on strength, is going to hit very hard compared to a player who is just starting out.
There are also weapon mastery trees. The more you use a type of weapon, the more experience you gain in that weapon type. As you gain experience, you can unlock active and passive skills in that tree. With the current balancing, it didn't seem like it would take ages to fully unlock a tree. Active abilities are stuff like, say, a special sword move where you spin around to hit multiple enemies, or an archery attack that rains down arrows over a small area (good for those 50v50 battles).
I spent an afternoon playing with a new character, and nearly made it to level 10. Of course leveling slows down the higher you get, but it didn't seem sluggish. Maybe 10 hours to get to level 20? That's the level at which you can buy your first house (you can own another at level 40, and a third at level 60).
So to answer your question more briefly -- no, it's not like PlanetSide. While a more skilled player can beat a higher level player, they are at a real disadvantage because their stats are lower, they have fewer weapon mastery skills unlocked, and their gear probably isn't as good. However, it doesn't seem like you'll have to dedicate your life to the game to level up. I went from level 0 to 10 in an afternoon. At launch, the level cap will be 60.