What do you recommend for a prospective student ?

They’ve both studied the same theories, quite similar background knowledge. But one is incredibly experienced and the other is pretty new to the world of supervision.

All else being equal, the more experienced one of course. :)

Look out for personalities, and the amount of guidance you will get. Basically the old PI will give you opportunities, but you will see them once in a month. The young PI will be available daily, and manage (and perhaps micromanage), and you will be more like partners. For my PhD I had an old PI for my formal supervisor, but the upstart PI for my informal supervisor - I was in her grant, and under her supervision, but she did not have the right to formally guide PhD students yet. It was the best of all possible worlds, because I got direct supervision AND the opportunities. I've got three papers out of it, and a stellar defense. I'm still friends with my old direct PI (ans she has her own lab now, based partly on our common work). The postdoc however did not go that well, but this is another story :)

To be fair, if you are seeing your supervisor more than once a month, this really is not giving you the independence you need.

This depends on the project. You would really struggle in molecular biology, especially in the early stages, if you only saw your supervisor every month. Mine popped into the lab every few days. He would ask me how I was doing; if I needed to check something, I would ask, if I didn't I would just say I was fine and carry on. This is a good approach in my experience.

My supervision was just like starryeyed described, and I liked it.

In my experience, I found the cooperation to be fruitful just because of the human contact. I did not need that much supervision, because I went to PhD after a research assistant post, but I needed reassurance - after the previous experience my self-esteem was pretty low. Scientifically, I did not struggle. Just like the TreeofLife said: often the "supervision" is just about noticing that the student's there.
Had I taken a PhD student that did not have research experience before, I'd guide him/her through the first year to ensure they get enough skill to cope on their own. Some things aren't learnable from thin air.
I'm in molecular neuroscience, so the methods are really tough.

I was talking about the PhD in general. Of course in the early few months you will use your supervisor more often but that should certainly change over time. I would not have tolerated my supervisor entering my workspace every few days beyond the first month or two. Mind you, by asking that question up front during the interview I would have known to expect that sort of supervision ;-)

I know what you're saying pm133, and this is probably a case of what works for one doesn't work for all.

I think an experienced supervisor knows when to get involved and when to hang back. As you said, the level of input changes over time and varies person to person depending on need. Of course if you're perfectly fine on your own and need no more input then it would be extremely annoying to have someone hovering around you all the time. I'm not talking about that.

It's just about giving someone the space to discuss their work when they need to. Coming into the lab is my supervisor's way of saying "I'm here if you need me", not "I'm here to check up on you". Plus, it's his work space too.

Luckily this style worked for me, but I'd have been fine if my supervisor had had a different style. I would just have got on with my PhD regardless.

I find that it is really impossible to make any kind of generalization about anything when it comes to supervision! It all depends on so many factors!