"hand something over to" or "hand over something to"?

Both structures are grammatical, and there is no difference in meaning between them.

When would one structure be recommended rather than the other?

If your noun phrase is short (like something or the prisoner), we would tend to put over after the noun phrase. If your noun phrase is longer (like someone such as a prisoner) we would tend to put over before the noun phrase.

One more comment: someone such as a prisoner isn't a long enough phrase for the position to make much difference; but for really long phrases, putting over before the phrase makes the sentence quite a bit easier to understand.

Over and to him should not be linked.

The combination of "to him" = preposition + pronoun. This can be explained as (i) an indirect object (ii) an adverbial modifier (iii) a (dative) complement

I...handed......it...over...to...him

S...…V…......O...Adv...prep...pronoun

Note how "quickly" or "reluctantly" can substitute for "over", or "over" can be removed altogether.

I...handed...over...it...to.......him

S...…V…......Adv.…O…prep…pronoun

Note how "quickly" or "reluctantly" cannot substitute for "over", although "over" can be removed altogether. This tends to indicate that I handed it over to him should be the preferred form.

Compare:

I...handed...the meal...over... the counter....to......him

S.......V............NP........prep..........NP.........prep…pronoun

I...handed...........him..............the meal...over... the counter.

S.......V..........Indirect Object........O.........[prep.........NP]

S.......V.........Adverbial Modifier......O......Adverbial Modifier

S.......V........Dative Complement...O.........Adverbial Modifier

These sentences have been done things to. There are two transformations (rules, alternations) involved here: Viz:

• Dative (aka Dative Alternation, Dative Movement, or Goal Advancement),

which relates sentences containing both direct and indirect objects, like

• They gave me the book.
  to sentences like
• They gave the book to me.

and

• Particle Shift (aka Particle Movement)

which relates sentences containing phrasal verbs like

• They looked up the book.
  to sentences like
• They looked the book up.

Both of these rules produce sentences with the same meaning.
And they can both be used together, provided they don't contravene some condition of one of the rules:

• They sent up the story to him.
• They sent the story/it up to him. (Particle Shift)
• They sent him up the story. (Dative + Particle Shift)

but not all possible combinations are grammatical, due to rule constraints

• *They sent him the story up
• *They sent up him the story
• *They sent the story to him up

And when you add pronoun objects, you can generate some really bizarre sentences

• *They sent up it to him
• *They sent it him up