Finally some people who can debate without saying ''Boo, you suck!''. Let me join this lovely discussion!
To get things straight, I am a 1.9 PvPer. I play Minecraft for around 6 years now and have played 1.8 PvP with lots of joy, although I was never great at it. I had good knowledge of strafing roding, using flint and steel etc, but I never really was great at using them. In 1.9 I would say I'm good. I beat most people, have a good K/D and know a lot about the strategies behind the PvP. Keep in mind I might be a little bit biased because of this and I might get some things wrong about 1.8 PvP.
In general I agree with most of you (I'm not really targeting this message at anyone). 1.8 and 1.9 require different kinds of skill and to say for either of them that ''it doesn't require skill'' or ''it's just spam clicking / timing hits'' is just simply wrong.
You can't determine which one is more fun, but I think you can have some agreement to which one more...in depth (I can't really come up with a good word to describe it). Compare it to Call of Duty or CSGO. I dislike CSGO, while I do like to play some Call of Duty from time to time. Still I would argue that CSGO is more competitive, has more strategy, has more interesting game mechanics and is just in general a better made game.
I still like Call of Duty better, as it is more casual. When I played CSGO I had to think constantly, it felled slow paced and I never really enjoyed it as much as just running around like a madman in Call of Duty.
You might see it coming: Compare Call of Duty and CSGO to Minecraft 1.8 and 1.9.
In general I would say 1.9 is the better game. Here's why:
Spam clicking VS timing
I don't think spam clicking is stupid, doesn't require any skill etc. but I do believe that the time frame in 1.9 gives players the opportunity to make an interesting game. While you can rod, use flint and steel and strafe in 1.8 the recharge time in 1.9 makes it possible to fake attacks, play mind games, read your opponent and use things like lava buckets, bows, shields potions etc. to create a really fun strategic fight.
I'm not saying you can't have a strategic game in 1.8, but the faster pace of 1.8 does limit the amount of strategy you can use in a game.
Additional items
As I pointed out you create a more strategic game with bows, lava buckets, shield potions.. and 1.9 really does improve on that. Don't know who said it, but the ''buff'' of these items, while weapons get nerfed is a good thing. Bows are more affective, but can bet countered by the shield, while the shield can be countered by the axe, while the axe can be countered by sword (due to higher DPS) and the sword can be countered by the...well, bow!
Punishing players for using items besides sword/axe. If you want to use a lava bucket then you have to wait 0.625 seconds for your sword to charge back up after using it, with a stone axe that is 1.25 seconds. This adds to the point that 1.9 is more slow paced.
The offhand enables you to use an additional item, like the lava bucket. No time needed. The offhand also offers a wide range of strategy. I once fought a dude, who used the left handed player option in combination with a sword in his main and a axe in his offhand to confuse me which weapon he was using, so I couldn't adapt the right strategy to his choice of weapon, as I couldn't really see what weapon he was using, just to name a great example.
Sword and axe
Moving on, 1.9 offers players to different weapons which play completely different. I'm not really bothered to talk about it in more depth as it speaks for itself.
Healing
To be honest, I think both 1.8 and 1.9 fail at making a good healing system. I dislike the healing of 1.8, as it takes ages to heal, making you vulnerable after every fight (+In a lot of discussion I hear 1.9 is slower paced, while I would argue that the healing of 1.8 makes 1.8 so, so, SO much slower). 1.9 removes the problem, but in full diamond fights with a stack of golden apples it is not PvP anymore, it is just 'break the guys armour' or 'let him run out of food', making it even slower paced than the 1.8 healing after a fight.
For full iron fights or full diamond fights with reasonable food (like chicken, not steak or golden apples), it is great, but no, if every 1.9 fight was full diamond with a stack of golden apples, I would switch right back to 1.8
Maths
Not really an argument, but just to point out: the maths of 1.9 PvP (Armour protection, sharpness enchantments, toughness) is a lot cleaner, although in the end it doesn't really matter.
Last but not least, 1.9 is and will always be the newer version. You can perfectly fine stick 1.8 or modified versions of 1.9 and further, but Minecraft has moved on from 1.8 (again this is not really an argument, but just to point out)