Better for one guilty man be set free, than one innocent man be hanged
Yes, I quite agree. But consider also the case where the person released is in actuality a serial killer. Then what is happening is you are enabling more innocents to die as a result of his being released.

It is that sentiment (Better for one guilty man be set free, than one innocent man be hanged) that leads me to suspect, though I don't have the evidence for it, that more of the guilty would be released if we have a death penalty than imprisonment.

As a thought experiment, let's take that sentiment - which again I stress I agree with - and downgrade it to 'wrongful imprisonment'

So it now becomes: Better for one guilty man be set free, than one innocent man be wrongfully imprisoned.

Not quite so clear, but I think I'd still go along with it, assuming we are talking about significant periods of imprisonment, not just a day or two.

Then let's make it mathematical:

Better for X guilty man to be set free, than for Y innocent men to be wrongfully imprisoned, but that is better than Z guilty men being set free.

or
X_guilty < Y_innocent < Z_guilty

When we are thinking about terrorist suspects, we seem to concentrate on the Y/Z part and accept that significant numbers of innocents can be detained to catch a very small number of actual terrorists.

Playing around with X/Y/Z is, I think, a worthwhile exercise because we all recognise the system is fallible and will wrongly release/confict sometimes. Deciding what proportions of each we accept says quite a bit about our own attitudes.