Combined with terrain multipliers and units with distinct reasons to exist, it breaks the central tenets of strategy down to their core, to the extent that I don’t realise I’m playing a turn-based title. Traditionally I can’t stand them, but there’s something about the recipe in Advance Wars that makes it a tasty, tasty treat.

Heroes of Might & Magic IV:
I think a choice is only interesting when it is supported by unit-balance or gameplay in general. If there is a “best” option given a situation then the choice is limited and if a choice leads you to always losing (such as non-Cyclops) then there really isn’t any interesting choice at all.

Fury et al:
Once again, I don’t class constant, varied and meaningless choices as interesting choices. Having a superficial choice is ok as a secondary part of the game, however there must be more depth.

I’ll check out games by Troika Games. +10 points for the Fury reference

Heroes of Might & Magic IV
This one stripped a bit of scope from the troop tree compared to HoMM3. They removed the upgrading of troops (Minotaur -> Minotaur Kings) and, on the surface of it, replaced this with either-or choices (Cyclops or Thunderbirds … choose one and lose access to the other).
This meant that players playing the same faction could field different armies. These are interesting choices, but in practice this dynamic was nerfed by poor unit balance … the player was forced into making a choice, but the choice came down to “I pick Cyclops or I gimp myself”, the choice had a high impact on your ability to succeed, but no value … it was no real choice at all.
On the topic of this game, this low-value choice was taken further by allowing the player to make up armies consisting of a band of heroes rather than a single hero and stacks of troops. These hero x5 armies could wipe the field even if the opponent fielded an army of thousands.
For choices, even interesting ones, to have value they must be supported, in this case by unit-balance. Many games pull this one off but as an example of something that did it particularly well; Dungeon Keeper provided constant interesting choices that were loaded with value to player.

Fury; AoC; StarWars X; Fable
Many games provide constant, varied and meaningless choices … they have no impact on the game. Fury’s Skills list where there were many and constant choices but they had little impact on the gameplay is an example. Likewise the gear available in Age of Conan had little to no demonstrable impact on the gameplay. These factors did impact the players experience as they were essentially ‘flavour’ choices and players felt that they mattered … up until it became apparent that they had no impact and then (some) players felt cheated.
Fallout 3’s companion choice for the final stages of the initial storyline had a real value to the player, until it became apparent that it didn’t matter, it didn’t impact the game to the extent they thought it might. Various games (Fable, a few Star Wars titles come to mind) feature player choices that are polarised as light\dark, good\evil etc and these have little or no impact on the gameplay … again, they appear to matter but then it becomes apparent that the player has been duped again.
Choices, even interesting ones, need to matter – see anything made by Troika to see how to implement interesting choices that impact the game and the users experience of the game.

It wasn’t so much the lack of units but lack of flexibility in the units. Each unit had a very clearcut role that the tech tree/cake improved on. If you look at a game like Go for instance, there is only one ‘unit’ type, the stone. Each stone has a myriad of strategic options though, especially when combined with the other stones on the board. This is what I felt Dawn of War II lacked. Although there was a rock-paper-scissors relationship between each unit type, there was no variation that allowed you to create new strategies by combining units. It was simply, ‘If you are fighting this unit, use this unit’.

I agree with the whole balancing act though. I find that indie and casual games are generally good examples of this due to their nature. You only have a limited amount of resources so you only choose a few core gameplay concepts and build the game around those. This in turn fosters a sense of doing more with less and keeps you from over complexifying but can also lead to the trap of not doing enough because you are so limited in resources.