To start with, you can probably expect the level of supervision to be similar, but then this should tail off fairly rapidly as you become more independent. During my masters project, I had regular weekly meetings with my supervisor. When I started my PhD (at a different uni so different supervisors), I had weekly meetings for the first two or three months, and then this gradually dropped off to about once a month for the next couple of years. In the last year/18 months I only really saw my supervisors if I had a particular issue I needed their input on, otherwise we just communicated via email for any small questions that cropped up.
However, all supervisors are different and some request a lot more face to face time with you throughout the PhD. I think it also depends on the student, as it is you who should be driving the project, and so to some degree you can determine the amount of contact you have. For me, I preferred to maintain contact via email as much as possible and didn't see the need for regular meetings, but other students may prefer to know that they have regular (e.g. monthly) meetings to fall back on.