Let's make this clear: Hippowdon can never, ever, ever combat Politoed, Celebi, Tornadus, or any of the other pokemon you mentioned in this post other than Dugtrio. Tyranitar can. Hippowdon can't stay alive against any of these pokemon because its OHKOd by all of them! What good is your recovery if you can't use it?
SpD Hippo can easily switch into defensive Politoed and Celebi, which is all it needs to do, as without rain, Keldeo, Torn-T and Thund-T become much more manageable. And don't try to dispute this, as it is a fact, not an opinion. Scald deals ~35% to SpD Hippo, and Giga Drain 37.5%, meaning that can he change the weather at will whenever those two are in, which is all that Hippo needs to do against rain teams, as it cannot wall their offensive threats anyway. It doesn't matter if it gets burned or toxic'ed in the process, because his job is to keep sand up, and as long as he does that he is already more useful than Ttar. But where can Ttar come into? A burned Ttar is a useless Ttar, so could luck switching into Politoed. Obviously you aren't coming against their offensive pokes too, so your only chance is against Celebi or Tentacruel, and you are still in danger of getting burned or getting worn down from Celebi's Giga Drain/U-turn.
Tyranitar is still a 100% counter to Ninetales even if it is burned. And most Abomasnow do not have Wood Hammer, and they are slower than TTar anyways. What is Hippowdon going to do to either of these pokemon?
I don't care if Tyranitar is a counter to Ninetales, as 50% of OU can counter Ninetales, as she is a support mon. What i do care about is that Ttar in no way counters sun, where Hippo definitely checks it better. Hippo is not afraid of Dugtrio, Genesect, and Ninetales as much as Tyranitar is. And yeah TtAr hates to get burned from WoW, as then it loses every hope of winning against the opposing sun team. You can't set up SR due to Xatu, you can't 2HKO Xatu burned, and you can't deal damage. So the only thing you do is switch the weather and lose 12% of your life every time you do so, while the opposing Sun team has their way with you. So yeah Hippo can switch into Tales much easier than Ttar, as he doesn't care about burn as much, due to Slack Off. Yes burn is a nuisance, but nothing more, as all that Hippo has to do is survive longer than Tales, which is not hard to do. Finally it seems that your knowledge is quite outdated. The most common variants of Abomasnow are the physical set with Leech Seed and Protect and the mixed with 4 attacks and Expert Belt. And both sets carry Wood Hammer, are faster than Ttar, and have enough power to OHKO Ttar with Wood Hammer.
As i said again, Ttar's best use right now is to counter Lati@s, and trap problematic pokemon for Keldeo, so that he can sweep. These are reasons to add Ttar in your team, not to win weather wars. When you are thinking about winning weather wars with your sand team, Hippo is the first poke that comes to mind.
Tyranitar can actually switch on Ninetales more easily than Hippowdon. The fact that it risks being catched by Dugtrio is unfortunately a shame, but Hippowdon that doesn't invest enough in Special Defense is going to take a lot from Fire Blast, even without sun. Also, Hippowdon is stil crippled by burn as not only its Leftovers recovery is negated, but its Earthquakes become much weaker. But even burned, Tyranitar can pose a threat to Ninetales, and a Choice Band Tyranitar can still OHKO 136 HP/0 Def versions of Ninetales with Stone Edge even when burned.
Also, I can't even see how can Hippowdon defeat defensive Politoed and Celebi. Tentacruel I can understand why, because of its weakness to Earthquake, but Tentacruel can still burn Hippowdon with Scald, and alias, Hippowdon is weak to Scald.
Hippo still takes a pittance from Ninetales fire attacks and has reliable recovery so it actually fares better than Ttar. Ttar gets burned on the switch and does what? Hit Tales with Pursuit for meaningless damage (Tales won't stay in to get hit from Ttar's Stone Edge), or fails to set-up SR against Xatu, or finally get trapped by Dugtrio, all while getting slowly killed from burn? Here is how much Hippo takes from Flamethrower, which is Tales's most common STAB move: 18.09 - 21.66%. So yeah he is very scared.
I never said that SpD Hippo beats defensive Politoed and Celebi. Don't put words in my mouth. I said that he can switch into them to change the weather without fear, unlike Ttar which gets fucked by a burn, or trapped by a U-turn from Celebi with Dugtrio.
I also agree with Venusaur for A Rank!