I think Sion AP build is the best. I've tried both builds Ability power and Attack damage.
I even think that AD is troll build :P

Start item : Doran's Ring
Then You buy another one , if your having troubles or want to deal more Damage early game buy 1 or 2 more.
Boot's Choices -Should be used 99 percent of the times to give you a stronger burst. - If the enemy team has too many cc or you need to be tankier- Alternative to Sorcerers boots -Recently popular item, I don't necessarily see the necessity to make the change from Sorcerer boots to boots of mobility. It's a good item if you are playing mid and ganking bottom and top often
Core items : or- Only buy Mejai when your sure that you wont die , so you could maintain stacks.
Final Items
or (Mostly for the statis active and extra AP)
If Enemy is Stacking Magic resist Buy Void staff.
Need more AP? Get another deathcap, the passive doesnt stack but you still get another 200 extra AP.

There is a dispute in the League of Legends community on which way you should build Sion.
You have the option of building Sion AD or AP. I have played both type and fairly aware with both builds. I will explain the pros and cons and my opinion on between the two.

AD Sion

People believe you should build Sion AD because of the massive bonus damage he can get from leveling his Enrage. His ultimate also gives you free attack speed and massive lifesteal. I don't personally find AD Sion a bad build. Its very deadly once you get your basic build down. The best comparison for AD Sion is Olaf. Like Olaf, once AD Sion has his basic core build, he can go beast mode on enemy teams. Mostly AD Sion benefits from the free AD and lifesteal from his ult.

AP Sion

AP Sion should be played as an AP carry tank. Your role should be more towards starting the party (teamfights) rather than following up unless you have a better initiation (Amumu, Ashe arrow). AP Sions great burst damage is most noticable and picks up once you hit level 10-11. You would have 2 doran rings and a couple AP items by then. Even with just those petty items, AP Sion can load punishing damage. However AP Sion is portrayed as a lacking AP carry because only 2 of his abilities benefit from AP.

Which is better?

Having played both, I do think AP Sion is the better way to build Sion. If you have tried both builds you should notice that AP Sion picks way earlier than AD Sion would. AP Sion needs levels on his Q and W where as AD Sion needs good items to be useful. Also, it is far easier to farm your enrage stacks with the AP build than the AD Sion build. Why go through the trouble of auto attacking when you can just press w and 1 shot an entire creep wave? I also find Sion's ultimate with AP Sion very good. If you have your basic build and lich bane. You could heal almost 600+ hp from one lich bane proc auto attack. This is very useful to heal your team during teamfights or to bait a chasing enemy.

In the end it is this, both builds work and are great. AP Sion just has more advantage over AD Sion.

Laning Phase

With getting a point in Enrage at level 1, your main focus is to get as much farm as you can. If you farm well enough it is equal to getting 200-350 extra HP by 30 min mark. You should try avoid showing aggression until level 3 or 4. And always make sure you do not spam your abilities. Sion's abilities drain extreme amount of mana. You will not be able to use your full combo when your jungler comes to gank.

By level 4-5, you should have farmed about 800-900 gold. This is when you should make your first b to shop. You should buy and and a couple HP pots and wards.

After you have 2 Doran rings and Boots. You can start showing heavy aggression and waste your mana a bit. The whole point of 2 Doran rings is to keep up your mana. Rather than popping your shield on minions to push the lane, focus on trying to deny and harassing your lane opponent. Your burst will take out about a quarter of their HP around level 5.

By the time you hit level 11 or 12. The laning phase should be coming to an end. You should have farmed enough to build a good amount of AP. Your main object by this point is to have a built. With Deathcap alone you should be able to annihilate enemy ad carry from full hp to 30 percent in one Q+W combo.

Team Fight Phase

The best thing about Sion is, he can somewhat tank and deal a lot of damage. There are not a lot of champions in LoL who can do this job. Because I main tank role in competitive play I enjoy playing Sion as a hybrid tank AP Caster.

If diving in to the other team is not considered a suicide, it is okay for Sion to flash into the other team to break a fight. Your main target during team fights should be to drop their AP carry or AD carry. Your burst will be so great that they wont even able to even stay in the fight and back out.

Also never waste your abilities, a misuse of your stun could have huge consequences. AVOID using your stun or shield to remove banshee veil. Sion only has two actual abilities. You cannot be wasteful with spamming your abilities like other casters.

Couple Playing tips

The way I like to play AP Sion is the hit and run style. You should charge your shield up, hop in stun + pop your shield and run back out. Of course there are exception to this, you could just axe them to death. But I usually avoid this tactic.

Use your shield to bait tower dives. Sometimes during laning, the enemies will find you a low HP and think they can kill you. So despite them having low HP as well, they will dive in to kill you and flash out. People often underestimate how much Sion's shield can tank. Time using your shield well so you can backfire the dying scenario back in their faces.

You should get at least 1 point in enrage so your farm can rack up additional hp.
Note that minion kills using your shield and stun applies with Enrage's passive.
This doesn't mean you should max enrage first.

If you look at my skill order, some of you will notice that I do not get a point in my ultimate until level 16. I do not get a point for my ultimate at level 6 because I find that you rarely benefit from your ultimate early game as an AP Sion. It's better to get extra damage from your stun. In higher level/ELO plays, its uncommon to end up in a situation where you will pop your ult and have a melee brawl with your opponent. Because AP Sion has such a crazy burst, you should try wearing your opponent down with your skills and finish them off with a flash, stun, shield combo.