Taric's a beast of a hero that brings some amazing **** to a team.
I main Taric and do very well with him (except for last game, I went 0/14/6 and have no idea what happened. Worst. Game. Ever). Here are some of the advantages Taric has over Sion.
Taric can be built cheaply. A solid build for Taric runs under 10k, so there's little need for him to farm super hard or get fed kills. My core build for him is Aegis, Chalice, Merc's Treads/Tabi and Spirit Visage. That ends up being like, what, about 6k gold? It's blindingly easy to get. Even if I'm being harassed really hard early game, I can get that kind of scratch without trouble. Anything beyond those items is gravy.
Sion is harder to build and needs mad last hits to snowball his HP. If he gets shut down early game he'll end up being useless. A beefy Sion ends up being a bus that rolls over your entire time and eats towers for breakfast, but that's going to be very hard to build. 95% of the time Taric will end up being well built and contributing more to the team than Sion.
Taric's ult is much better than you give it credit for. Once it's toggled on, it won't go off until you cancel it or get killed. CC can't interrupt it. Silence won't stop it (it will prevent you from turning it off, which can be annoying). 50hp/second to everyone around you is pretty big, especially if they have Spirit Visage. It also heals creeps (gives them a portion of the damage buff, too. I think 1/4) and gives your team a huge damage boost. If you keep it up for 10 seconds during a team fight, that's +500 hp and +45 damage to everyone on your team for 10 seconds. It's like giving everyone on your team a free BF sword and giant's belt every freaking fight. So badass.
Given that it has a low cooldown, it can be used to give people some quick healing and is great for toggling while the team's being chased. Once again, 10 seconds would give everyone +500 hp as you flee from a fight. I can't count the number of people I've saved with Taric's ult. Team mate got ignited during a close gank? Stand next to them with your ult on. Seriously one of the best ults in the game. It does require finesse to use. Knowing when to cut it off to keep the rest of your mana pool intact is very important and takes some experience.
His heal looks a little weak on paper, but is actually quite strong when you think about it carefully. For one, it always heals Taric. If you're targeting someone else, you're dishing out 540 HP worth of healing every cast, more since most Tarics get a Spirit Visage. Suddenly it's not looking so weak. The cooldown on his heal is reduced by 2 seconds every time he auto-attacks anything (hero, minion, structure), which can make it godly for pushing. It can also be used on minions. Have a siege minion with you? Imbue + Radiance will let that bad boy tank the tower so long as you have mana. You can still dish out heals at a decent clip in a team fight so long as you can hit something to reduce the cooldown. Stark's, which you usually get anyway, gives a decent chunk of aspd which helps with this.
Since Taric's so team-centric, he's a fantastic lane partner. He heals both himself and his lane mate, gives them armor and can initiate with stuns. If you're laning with a DPSer or another stunner, it's very easy to harass the enemy or continually kill them during the laning phase. The reason a lot of Taric players (me included) pump shatter is because Dazzle + shatter by itself is a huge amount of virtually risk free damage. Dazzle + shatter + armor debuff + phys DPS lane partner = kills. He also matches up with most heroes during the laning phase. Taric + phys DPS is godly. Taric + tank is godly (lol Taric + Alister). Taric + caster is godly. Actually, Taric + Sion is one of the best lane combos in the game (chain stun, chain shield shatter, heals, gg).
So in the end.
Above average survivability.
Very hard to shut down.
Great aura support (shatter, ult, items).
Cheap to build with an item build that scales well.
Very flexible and powerful lane partner.
Synergizes extremely well with other team members.
One of the best pushers in the game.
Requires some teamwork to be successful.
Above average survivability. Great if he can snowball well.
Good 1v1 fighter.
Can become a bus.
Good lane partner. (his stun is great, coupled with a shield pop it can dish out serious damage. No heal hurts him in comparison to Taric).
Has to snowball to be good.
Moderate - expensive item build.
Doesn't really buff the team (his ult kind of does, but it puts him at risk to use it and is inconsistent).
Easily shut down, especially in team fights.
They're both good heroes, but Sions big weakness is his heavy reliance on snowballing. In higher ELO games, people will keep him locked down and he'll be drag the team. For TT, however, Sion's an amazing pick while Taric's considerably weakened. Aura's aren't as good on TT and Sion's a lot harder to shut down. He's better 1 on 1 and in small fights, which is what TT's all about, making him the perfect balance of hard CC, survivability and damage.
Bear in mind that you might just suck bad with Taric. I suck bad with Gangplank. I played like 60 matches with him and just can't figure the hero out. Almost every other GP I've ever seen does much better than I do, but I've never really been able to figure out why. If you're playing better with Sion, keep playing Sion. I love GP to death, parrrrlay is so much fun, but I had to accept I can't play him and move on. You could also be building Taric incorrectly. DO NOT max dazzle first. Who cares about a little cooldown reduction? How often are you casting dazzle each and every time it comes off cooldown? Never. Shatter and imbue are much stronger skills to level early on, and I can garauntee you'll never need to chain stun in the laning phase. I favor shatter over imbue, but it's largely a matter of personal play style and lane comp.