Rain Dance is bound to be useful, due to the fact that Water Pokemon generally benefit from weather with their powered Water attacks, and Pokemon whom are weak to Fire will find the damage less punishing. Water-types generally learns Ice attacks, and thus, Grass-types aren't even able to ward them off. There are also some interesting Swift Swimmers and Dry Skinners (Parasect and Toxicroak), and they are usually Water-types. The only non-Water that I see got Swift Swim is the Polar Bear Pokemon. Let's not forget Hydration's drawback-free effect in Rain, of course. Added to the fact that Politoed is a capable Pokemon (good bulk) that can set up Rain, and it's probably a very stable playstyle.

Sunny Day, on the other hand, doesn't have any Chlorophyll Pokemon that benefits from a Fire attack, because they don't get STAB off it, and more importantly, they are hit hard by Fire attacks themselves. Fire Pokemon doesn't have a means to increase Speed in the sun, but they are still threatening in the Sun, especially when Water attacks are not as effective anymore. The Sun has perks, thankfully. Any weather recovery move becomes a benefit, since it heals more. Also, Solarbeam, a very strong Grass move that even Fire-types can learn is basically a free attack. Perhaps the most important aspect of Sun is any Pokemon that learns Growth. This is because Growth gets a huge benefit in the Sun. One use in the sun, and your Pokemon gets a huge boost in both Attack stats. Mixed attackers like Tangrowth and Shiftry would love this move because they have Chlorophyll and good Attack stats. Fast and Powerful Fire-types like Blaziken (Speed Boost) and Heatran (Choice Scarf) would benefit from the sun to provide powerful Fire attacks. Ninetails is not a bad provider of sunlight, since she is not weak to Water attacks and can use free Solarbeams right off the bat.

However, both weather teams have the same common enemy: Sandstorm. The only two users of Sandstorm are not only competitively viable, but also not too broken that they are ban-worthy. This means, a sandstorm team would have the option to carry two Sand Stream users to ruin the fun of either one, but carrying two legit Drought users is not viable (Vulpix is certainly not going to stand on her own), and there's only one legit Drizzle user. Basically they are outnumbered. Fortunately, Water and Grass moves are a bane to the users, and Sun has Tangrowth for example as an obstacle (unless Tyranitar happens to be a Special variety), and Rain has plenty of Water users to dampen the sandstorm initiators.

That said, I prefer Sun, because they have all the fun Grass Pokemon to play with: Mixed Tangrowth, Go Ahead/Butterfly Dance Doredia, offensive Mebukijika, mixed Victreebel, Special Exeggcutor for example, not to mention that to me, it's a very unique playstyle compared to Rain.

Thanks for reading.