The best way I've ever seen it phrased:
"The controls and interface for a game shouldn't obstruct play, but enhance it."
The ability to play a game can be broken down into the mind's ability to strategize, evaluate, and react; and the body's ability to perform the desired actions. We'll call these general categories "strategy" and "dexterity". If the amount of dexterity needed to play a game is low, then all of its depth must come from strategy, and vice-versa.
People enjoy different kinds of balances between these two. Fighting game enthusiasts generally appreciate a healthy balance between the two, making it a sort of test of both mind and body. Personally, I find these types of games frustrating, largely because I don't have the dedication to practicing the controls. I prefer fighting games with more simplistic controls, even than Street Fighter--Smash Bros. and Soul Calibur are my games of choice, as any move can be executed without having to press more than one or two buttons at the same time. Are these games less strategic? Less rewarding? Yes and no, depending on the player--but they are my personal taste.
But of course, we aren't talking about fighting games, we're talking about a real-time team-based tactical RPG. This genre tends to introduce a certain degree of inherent complexity; certainly, there are a very large number of factors to be considered at any given instant of the game. I believe it is the common opinion of the community, and indeed apparent in many of the design decisions made by companies that make such games, that the difficulty of such a game should primarily arise from mental difficulties rather than the interface or controls; there are enough factors to be dealt with as it is.
So then, with it established that we should be looking at tactics and strategy from a mental perspective, we should next determine upon what scale strategies should be compared. As any experienced player would tell you, Demigod is very much reliant on judgment; a player must constantly be asking himself, "Will I be able to defeat this enemy in time? Can I hold out for reinforcements? Should I chase him that way? What skills/equipment is my foe using?" and so on. Should the player decide correctly, they are rewarded with power and wealth; incorrectly, with death and defeat.
Therefore, an appropriate scale against which to appraise strategies in Demigod would be from a risk-versus-reward standpoint; that is, strategies higher in risk should generally grant more reward. As an example, assaulting an enemy until they are forced to retreat, and allowing them to do so, rewards the player with briefly unrestricted ability to farm and gain strength; pursuing that foe dangerously close to their tower line to finish them off is much more risky, but if correctly executed, yields a substantially larger experience and gold reward.
It is a logical assumption that more skilled players are more likely to successfully capitalize on high-risk strategies, thereby reaping higher reward, and in addition, more likely to correctly determine their likelyhood of success in a particular risky venture, as well as that strategy's reward. Obviously, some strategies have tremendously high risk and very little reward--for example, trying to rush the enemy's heal crystal at level 3 and "spawn-camp". Therefore, the skilled player can also eliminate strategies that do not yield satisfactory risk-to-reward ratios, and will only employ those that do.
However, the depth of a strategy game can arguably be measured by the size of this "satisfactory strategies" pool; if the pool is too small and too shallow, the game can become largely formulaic. The larger the pool, the more strategies one can choose from, depending on the situation; victory goes to he who correctly identifies which of the multitude of strategies yields the highest return, then executes it to the highest degree; if two players use equally rewarding strategies against one another, the one who executed theirs best should ideally win.
To maintain the balance and "depth" of this pool, all viable strategies should have a roughly equal balance of risk to reward, when all factors are accounted for; some may be better in certain situations than others, but no strategy should be the best in a majority of circumstances. The caveat to this is, situational details might augment this ratio one way or another--a strategy that is high risk against certain Demigods might be low risk against others, yet both yield the same reward. This may seem objectively imbalanced, but this is where the team factor enters the equation: the compensation for having a disadvantage aganist a given Demigod or situation, is to have a teammate who is strong in that area. Because each Demigod has natural areas in which they are strong and others in which they are weak, one must adjust one's team in order to compensate.
This presents the altogether more frustrating problem of relying on teammates to choose their character in the interest of team balance rather than personal taste; however, because this is a human factor and not a game factor, the issue of balance is now largely reliant on skill; that is, if you wish to overcome the strengths of a particular Demigod, either choose your character such that you have an advantage, or play with teammates that will choose a character that compliments the one you want to play, particularly against that Demigod, and vice-versa.
With this treatise established, we can now more clearly assess the balance of Unclean Beast; rephrased in this established terminology, the OP's post suggests that the Unclean Beast gains disproportionately large reward relative to the risk he must undertake; as a result, it takes less skill to successfully exectue these stratagems and reap the same reward as a more-risky stratagem of a different character.
Is this the truth? It's difficult to say. Many have put forth ways of dealing with the beast, but none of these answers appear to be satisfactory to the OP. Perhaps, then, we are not giving sufficient weight to counterstrategies; perhaps it is not that UB's strategies yield too much reward for their risk, but that the UB's opposition has not determined how to make those strategies sufficiently risky as to discourage their use. Perhaps that, then, should be the focus of debate.
Ultimately, I would say the fastest way to determine the balance of the Unclean Beast is to play many, many games using him, and see what beats you and why. If you can develop a counter-strategy to that, do so, and see if that can be foiled. This is a healthy way of developing the strategy of a character; the winner is then determined by who can stay a few steps ahead of their opponent in the game of strategy and counter-strategy, then capitalize on that opportunity. I know it worked for me and my undue hatred of Regulus. 
