For a very long time Phoenix Udyr was the only way to play him. Tiger was useless before its buff. Experienced Udyr players almost considered the skill a joke. After it was finially reworked it became Flavor of the Month. While it was strong the effectivenes of the Phoenix was never diminished. While both are viable in the current meta Phoenix stance offers some distinct advantages that tiger cannot.

Tiger udyr has an extremely strong early game. The early game damage on tiger and its relatively low cooldown makes it easily one of the strongest burst nukes at level 1. The ability itself has good scaling but sadly Udyr can rarely take advantage of this. As a melee champion with no gap closer Udyr generally needs to run right into enemy champions to be effective. Building damage to take advantage of the scaling leads to extreme squishyness. Because the burst is so good you will want to quickly take out squishy targets but a Udyr with no defense will most likely die before he gets in range of a mage carry or a ranged carry. As a result like it or not you will most likely be building a good deal of defensive items. While a few defense items have attack damage incorporated for the most part Udyr players will not be able to take advantage of tigers scaling. Another folly of Tiger Udyr is that none of his other abilities scale with AD. The ability is overall strong but it lacks practicality in large team fights as it requires Udyr to build around it.

Phoenix Udyr is an entirely different beast altogether. The AoE from the ability allows him to jungle extremely quickly. Many claim that Tiger jungling is only a few seconds slower but a optimized Phoenix route is much quicker. I personally have cleared the jungle (golem, wolves, wraith, lizard, small golems) by the 3:30 mark. Yes this is possible, and if you follow this guide you too can achieve a similar speed. Another great aspect of Phoenix Udyr is the freedom you have while building him. You might have noticed already, but this build does not include Wriggles Lantern. While an extremely efficient item not needing to rush it allows you to do all sorts of interesting things, and the best part is that it doesn't even sacrifice jungling speed! The third hit passive on Phoenix can deal great burst and is much more sustained. Phoenix also grants bonus AD/AP a often overlooked effect. This will increase dps substantially, reduce the need to build offense as much, and lastly provide a slightly stronger shield while transitioning to turtle stance.

Attackspeed is the optimal choice for marks and quints. This is very important! Udyr is a deceptively difficult to play champion with many small ways to optimize his abilities. For example his Passive Monkey's Agility will give attack speed and dodge and stacks three times. This ability is extremely important for optimizing his jungle speed. Phoenix stance will shoot a bonus wave of very high damage every 3rd hit. With attackspeed runes and a full set of marks and quints and some good timing you can use this part of phoenix twice before having to change stances to renew stacks on Monkey's Agility. This will improve jungling time SIGNIFICANTLY.

Armor seals are mandatory, but for glyphs you may take flat Magic resist if you prefer. I like to go with MR per level as it surpasses flat MR at level 10 and because you spend alot of time in the jungle you wont need it as much as a laning champion early game.

R>W>E>Q with a point in Bear at level 4. This is generally what you will want to do but feel free to make changes based on what is happening in the game. Adapting is very important with any champion and static set builds will often result in loss. For example an extra rank early in Bear if you are doing well will help you chase down enemies faster. A point in Tiger at level 11-12 might help you push a tower better etc...

Smite is a given, but you can play either with ghost or flash. Ghost is great in a casual or low-medium elo environment. I recently started using flash on Udyr much more often as 1800-1900 Elo can be very unforgiving and flash is often the get out of jail free card that you need to survive. Ghost is however, much better at chasing down enemies.

While most junglers that start with cloth transition into Madreds i find it does nothing to increase jungling speed. The reasoning behind this is that the AoE from Phoenix will generally finish killing everything at the same time. Thus focusing one monster down and switching to the next one wont matter because the other two will still die from the flames at the same time. Udyr does not need the life steal due to turtle constantly shielding him from damage as well as healing him in the process. While the ward is nice, you can easily get by the old fashion way of just buying wards in the shop. Perhaps the strongest part of not building Madreds is you gain the ability to build other items out of your cloth armor. Ninja Tabi is an extremely cheap boot and the dodge can synergize well with Udyr's passive as well as the nimbleness mastery. This will also make you much, much faster than most other junglers at this point in the game. What Tiger Udyr gained with the extra burst damage during ganks, Phoenix udyr can easily make up with ridiculous early game movement speed to help chase down those escaping enemies and close the gap in ganks. No one else at that point should have tier 2 boots and the movement speed mastery, nimbleness, bear stance buff, and ninja tabi should still allow you to easily out run the ones that have a tier 1 boot. This should land you an easy kill or a kill for your teammate.

The next item you will want to rush is a Sheen. You can build either the amp tome or the mana crystal first. Few people realize that Phoenix stance actually scales extremely well with AP. It fires off 5 waves of fire each with a .25 ap ratio. Getting all ticks in means a 1.25 ap ratio, one of, if not the highest ratio for a standard non ultimate ability. In addition the 3rd wave of fire also has a .25 ap ratio. The sheen will also grant very good burst/sustain as Udyr is a champion that constantly uses abilities in teamfights. This item is core because it increases mana (Udyr can be quite mana hungry early and mid game) gives ap, and most importantly the passive extra damage. From there you will want to build defense. If your team is doing really well you might want to just finish up Trinity Force. Zeal will help run down enemies, Phage will help you be slightly tankier, once again build depending on whats happening in the game. A early negatron cloak can make up for the MR you lost from not building merc treads and will help you survive alot more burst in early teamfights. You will generally want to build it into a banshees but because you dont need the catalyst i will generally build other items before completing it. A sunfire cape is useful for the armor and most importantly the HP. When you are tanky enough to rarely die in teamfights and feel like you need more damage a guinsoos is a great choice. The attack damage and AP will significantly increase DPS as well as the attack speed letting you proc Phoenix much more often. The stacks are very easy to keep up on Udyr for obvious reasons. DO NOT RUSH THIS ITEM. You need defense first for it to be effective. At the end or near the end of the game you may want to sell Ninja tabi for Merc treads. Overall merc are much better boots but they are expensive and rushing tabi can help you get off game changing ganks during the first half of the game.

My route for jungling is:

WOLVES>BLUE>WRAITHS>LIZARD>SMALLGOLEM

Positioning is EXTREMELY important for Phoenix udyr. The 3rd proc fires out a cone and to ensure best jungling you must make sure you hit all creeps with it. Experiment with it for a few games it can be a bit tricky to get used to. Start at wolves. Unlike many other junglers you can kill them all before blue spawns! If done correctly they will all die at 1:50. Run to blue have someone leash it. Then get wraiths. Smite will not be up but you dont need it! Do red then smite small golem. From there you have three options: Back and get boots, get wolves camp again, or gank with red and blue. Udyr is an extremely competent counterjungler. If you are against someone like lee sin that spends alot of time early game ganking and often doesnt take blue or red first trip feel free to steal their jungle.