Berserkers have an extremely difficult time at level 60 pvp. It is true that anyone who wants to run away from you can easily do so, which is the product of no ranged attacks/teleport attacks/efficient gap closers. Not everyone tries to run away though, on occasion people will actually fight it out as there's no penalty for losing unless you are outlaw mode.
Like Easymode said, Warriors are all but impossible for a zerker to beat. Backstab completely negates a zerkers ability to block and lets them get a few free hits in on you every time it's up. Experienced warriors also know to dodge right as the stun wears off to avoid any attempted counter attack. Unless the warrior isn't very good, doesn't know how to fight zerkers, or makes a series of big mistakes, you pretty much can't win.
Slayers are a tiny bit more manageable, but not much. If you have exceptional reflexes you can turn and block after a Slayer uses backstab, since it's a root and not a stun, but realistically most of the times a slayer will get a hit in before you do. The real problem with fighting slayers is that their hard hitting attacks are a lot quicker than yours. If you try to charge an attack, you're going to eat damage, and if they're any good they can easily dodge your horrendously slow attack animations.
Lancers are pretty strong against zerkers, but make for a more competitive fight than the previous two. They will typically block everything they can and try to chip away at your HP whenever their stuns are up. Played well there's nothing you can do against them, but the fact that they take much longer to kill you than other classes means they will most likely make a mistake eventually. If you can take advantage of that and get a few good hits in, it can change the way the fight plays out and you can sneak a win.
Archers and Sorcs are similar encounters to a zerker, you'll be using block a lot. If you are patient and know what to look for you can win most encounters. The key is really to block off their big attacks then trade damage from their smaller attacks to try to dash in for a knockdown or big hit. They both are capable of big hits so if you aren't careful, you'll find yourself in trouble, but overall they make for competitive encounters. However, this only applies in the event they stick around to fight. If they decide to run, they can easily do so.
Mystics and priests are not as similar as you might think. I haven't fought as many of these, I'm not sure if that's just random circumstance or if it's a reflection of their difficulties in 1v1. In my limited experience Mystics will try to dot kite you. Like Lancers this makes for a very slow fight, and their dot is easily blocked. The real problem is just getting close to them to do any damage, they don't really need to stand still very long for just about anything. If you do catch up, you need to knock them out fast or they'll get a heal fairy out and you'll have to start again from the top.
Priests have a few semi hard hitting close range attacks, which makes for an interesting fight if they try to use them. Some priests will try to damage trade with you, then explodey jump away and self heal. It's pretty effective if done right, but it also gives you openings for a second knockdown or a lucky crit to finish them off. Similar to mystics, if you don't finish them off in a quick burst they can easily heal back the damage. Like I said I haven't fought many priests 1v1 either, so it's possible they have some other tricks I'm not aware of.
Also, the Lancer, Mystic, and Priest scenarios change drastically if they have 30% reflect damage, in which case the encounters move from the "competitive" category up to "virtually unwinnable" with warriors. I'm still holding out hope that this stat will be nerfed, though.
Berserkers are a lot of fun to pvp with imo, but they can be a real source of frustration. Some classes will be almost unbeatable, and most classes can give you a good fight. If you want to gank people, this isn't the class for you, as they're ridiculously easy to run away from. Berserkers are better in group pvp than in solo pvp, but not necessarily any better than most other classes. The theory goes that if you have another class using stuns, roots, or knockdowns to set targets up for your big attacks then berserkers can be amazing, but realistically in a group setting any target that gets stunned and focus fired by several people is going to die; a berserkers big hits aren't a necessity for that strategy to work.
In conclusion, I am of the opinion that you should only play a berserker if you REALLY LIKE playing a berserker. They can be incredibly fun, and are competitive with most classes to varying degrees. However, you have to be able to accept the fact that you will never win a 1v1 tournament based only on your class, and no amount of skill is likely to change that. You also have to accept that people will easily run away from you if they choose to, and you will rarely if ever be able to run away from anyone else.