Air Dragon and Water dragon seem like the best examples of this dichotomy (that is, each dragon's buff is helpful for a particular strategy, but also strong against that strategy) but the other two don't seem to follow that guide as well.
Fire dragon buff seems to just overall be "higher offensive power", which arguably benefits a team that wants to fight OR the team they're fighting, but it doesn't benefit different team compositions equally. A highly tanky team, or just an early-game team that wants to overpower with base damage, would have much lower benefit from the AD/AP multiplier since they don't purchase as much to be multiplied, nor would they benefit much if they did. A straight-up damage multiplier, or some penetration (total armor % penetration would make it effective regardless of enemy team comp) would (imo) do a better job of being appealing to all champions rather than only having value in denying the opponent for some. Having it only apply against enemy champions would also help focus it as a "teamfight" buff rather than just making carries stronger at everything. Alternatively, having some special effect when an enemy champion is CC'd might do an even better job; not saying this particular implementation would be perfect, but something like gaining movespeed for every nearby enemy champion affected by CC would make it desirable for both engaging or disengaging, bringing it in line as the buff that you want if your team wants 5v5 teamfights, while also being a buff you want yourself if the enemy wants to engage on you.
The Earth dragon buff misses the mark even more. Bonus damage to objectives rewards offensive sieging, or rushing neutral objectives (such as sneaking a baron while the rest of your team sieges offensively, or if you want to siege but even with Earth dragon buff you need more power). However, it has no power at all defending against a siege, and very little when contesting an objective that the enemy already started. The only situation where it "counters itself" is if objectives are being traded: the team that is better at taking objectives wants to emphasize their win condition, while their opponents can use the buff to bring their objective taking power to a more competitive level. To phrase it differently, it's a buff which only encourages tower/objective trading, rather than contesting which was one of the main objectives of the changes in the first place (or so I'm told). Again, I can't guarantee that this particular thing would be a good implementation, but I think that a better option would be if the Earth dragon gave a buff which either activated at those objectives but only affected champions, or which only activated while near one of those objectives when an enemy champion is also involved. For example, it could grant a shield like the 2nd tier side lane turrets. For a team that wants to make aggressive objective-focused plays this would discourage the enemy team from contesting because of the advantage you get, while a team that is defending against that style would have the edge they need to stand on even ground with the team that otherwise had the confidence to be aggressive.
I'm looking forward to seeing how the Dragon Chroma Pack impacts professional play, but I'm also interested in one more thing: There have been some vague mentions that the spawn order of dragons is "not purely random" i.e. it isn't just a 25% chance of each at any given spawn. Is there any more information about that? Like, is it weighted to be less likely to provide streaks or large stacks of a single dragon buff, or the opposite? Or maybe it's dependent on how long the previous dragon went unkilled, so a hotly contested dragon type is likely to come up again while one that could sit for a long time is undesired so won't show up again? Or maybe the game attempts to analyze the compositions themselves and provide its best guess for the popular dragons?
