Is anxiety as hell-bound as cruelty?

(N.B. This is from a Theravada perspective)

If a person is all three (i.e. gentle, loving, anxious, and longing) then what determines their future rebirth?

Karma is a complex system; there are three sets that you have to understand, one mentioned by Sankha:

By order in which they operate:

1. weighty karma
2. karma performed at death
3. habitual karma
4. other karma

By their function:

1. productive of new results
2. supportive of other results
3. destructive of other results
4. detractive from other results

By the time it takes them to bring results

1. in this life
2. in the next life
3. in some future life
4. already finished

So, to say that behaviour X leads to hell is just a simplification - it should be taken as a guide, not a dogma. The Buddha himself said:

“Therein, Ānanda, when a recluse or brahmin says: ‘Indeed, there are evil actions, there is result of misconduct,’ I grant him this. When he says: ‘I saw a person here who killed living beings…and held wrong view, and I see that on the dissolution of the body, after death, he has reappeared in a state of deprivation…even in hell,’ I also grant him this. But when he says: ‘On the dissolution of the body, after death, everyone who kills living beings…and holds wrong view reappears in a state of deprivation…even in hell,’ I do not grant him this. And when he says: ‘Those who know thus know rightly; those who think otherwise are mistaken,’ I also do not grant him this. And when he obstinately adheres to what he himself has known, seen, and discovered, insisting: ‘Only this is true, anything else is wrong,’ I also do not grant him this. Why is that? Because, Ānanda, the Tathāgata’s knowledge of the great exposition of action is otherwise.

--MN 130 (Bodhi, trans)

Why are 'anxious' and 'cruel' both reborn in hell?

Orthodox Theravada theory says that, in general, anger leads to the hell realm, greed leads to the ghost realm, and delusion leads to the animal realm

Anxiety could refer either to worry or fear. If it refers to worry, it is a delusion-based state and will incline one towards the animal realm. If it refers to fear, it is an anger-based state and will incline one towards teh hell realm. Note that simple worry and fear shouldn't lead to either realm, unless it is serious enough to lead one to break precepts - harming others or oneself out of fear or worry. Taking strong anti-anxiety medication might arguably fit the bill (leading to animal realm); killing or stealing could lead one to hell, and could ostensibly be performed out of fear-based anxiety.

Cruelty is anger-based, so yeah, always inclining one towards hell.

Isn't someone who is cruel more harmful than someone who is anxious, and therefore more 'deserving' of hell?

One would think so, probably because we use the word anxiety to refer to a mild form of anger (fear) or delusion (worry). These states can, however, become intense and destructive to the point of suicide, drug addiction, etc., which can in turn easily be more destructive than mild forms of cruelty, like insensitivity to the feelings of others, etc.

Is an anxious person reborn in hell because anxiety a hellish (unpleasant) experience, i.e. if you choose to live a life of anxiety you're therefore inclined to choose to be reborn in hell?

Unwholesome-inclined individuals don't really get the chance to "choose" where they are born. Somewhere, the Buddha is said to have taught that it takes morality for one to have a stable enough mind to actually choose where one is born, IIRC (can't remember the source off-hand). But yes, the general idea is that one's prevalent state of mind inclines one towards hell; it doesn't have anything directly to do with the judgement of others.

Do cruelty and/or anxiety correspond to kilesas?

Answered above.