The only thing that can burst you fast as a Priest is a Rogue or Arms Warrior. Hunter's you can invariably LOS, and the same goes for Mages. If a Warrior or a Rogue is nuking you, all you can rely on is your partner for a peel or PS. Improved Inner Fire is a MUST in 39 arena. With the glyph and talents your running around with 30-35% armour, with enough charges to last you most games.
Taking a disc build with out IPWS, or Mental Stength leaves you with more stress on your mana pool, and too much pressure to heal through times when PWS is not up. The glyph of PWS obviously compliments the talents and reduced CD. Reduced CD on PWS means the Rogue has more opportunities to vanish inside it.
Dispel glyph gives 3% of maximum HP, so on a 3k HP Rogue, that's 90HP per Dispel. Improved PWS shield + glyph gives 20% of 440HP. Which is 88hp. As for which is better is a preference. Dispel is going to give more overall healing HOWEVER, PWS is not consuming a GCD and is healing over a greater time range. An argument for PWS iS, the 20% is ALWAYS coming when you are under damage, where the dispel healing may or may not be occuring on damage taken. The converse is that Dispel is going to provide more overall healing.
Silent resolve is a talent which I'm not sold by at this level, in the same way I'm not fully convinced by the druid talent Subtlety. At 80 you can afford to take these talents, but at 39 there are better talents available which do not rely on RNG. (Mental agility should always be taken over absolution, unsure why i specced in those 3 points).
The first build I stick by, just with a switch in Mental Agility. Priest builds at this level are very dependant on the arena partner. I play rogue, so for us we play super aggressive, but at the same time if we do get counter CC'd i know he can last, as can I, with nearly 3400hp buffed. I might even consider
The World of Warcraft Armory - Improved Mana Burn should be taken but generally our games go along the lines of either full CC control or getting the opposite healer to blow their mana pool healing. My Priest generally uses his mana to burst/dispel only. If you are running a more defensive setup, Imp Mana Burn is not optional.
The second build is a holy healing crit build. Generally we are using lesser heal where possible. It provides good mana efficiency, range and crit, with a good compromise in survivability.
Third build is aimed at max damage, range, crit, and casting speed on Holy Fire. It's purely an aggressive build.
The fourth build is great - it's something a little different to your normal builds. What you are looking at is a high survivability/CC build with the staples of mindflay, silence and reduced CD on PS. If you are good with co-ordinating CC it's a great build, but provides good survivability. The VI works as a weak renew, and it's an AOE heal.
The trick at 39 is to consider what you are playing with. The ideal partner for a Priest is a Rogue, and at 39 this is no exception. Very few teams can beat it if played properly, and the specs above are tailored to that. Please have more respect before you talk about 'terrible' builds without considering the thought process behind it.