Is it advisable to give a handout with the slides to the jury of my PhD defense?

In my department, students usually give out a handout with slides to members of the committee. Many seem to find it helpful - they use it exactly as you said:

to take notes, to follow the slides (slides are projected above my head in the amphitheater) or to go back if they missed a step

They also use it in other ways - for example, if they want to ask you a question about a previous slide, they can refer to the handout to say "Can you please go back to Slide 5" instead of having you flip through the slides one at a time and saying "Stop!" when you reach the one they're looking for.

Some don't use the handout at all.

In all of the defenses I have attended, I have never seen a committee member get distracted by the handout, or read the handout instead of paying attention to the speaker.

So, based on my experience I would consider the handout to have some potential benefits, and very little or no disadvantages.

My answer: do provide the handout.

There are two cases that I considered before giving the answer:

Easy case

The answer is easy if handouts are traditionally provided at PhD defenses in your department. You do not want to spoil the mood of your committee by taking away something they are used to. They will not fail you over this, but who knows how they come up with any extra work they want you to do before signing the dissertation.

This is the case in my department; traditionally, each member of the committee is given a handout with six slides per page and a pen.

Harder case

If handouts are not traditionally provided in the department, I would still opt to provide them. To me, the pros you provided outweigh the possibility that a committee member gets distracted. Every professor in your committee has sat through hundreds of academic talks; if they want to pay attention, they will be able to do so.

Final note

Make sure that the handouts look good; this may mean making a separate version of your presentation for the handouts. Specifically, make sure that any animated slides show up well in the handout. Depending on presentation software used, animated slides tend to either get compressed into one slide on the handout, or split into dozens of them—either case is usually not what you want and needs to be fixed.

Since it's a PhD oral defense, I would say no. The jury has read your entire thesis and probably took notes from the text. They don't need additional material.

Note : This answer is only applicable for system where the jury received the thesis before the defense (obviously).