There is no reason, once out of warranty, to go to the dealers for service unless you need something specific that only the dealer can provide. That could be a service that requires a special tool, or one that requires special knowledge, or maybe you want someone with ready access to parts so your service doesn't take days waiting for parts.
I too have an '01 and I had my 60k done at an "independent mechanic" who specialized in Porsches, who raced them and who had around a dozen he was working on that required much more serious surgery than my simple services were likely to need. He did an excellent job.
But if your "private mechanic" is just a general repair guy and he doesn't specialize in Porsches, then will he know what to look for as the 60k consists of many inspections. When you take the car in for service, you are depending on the experience of the mechanic to look at the condition of various parts and determine honestly if they need (or when they will need) service. Without your mechanic having that knowledge gained from many years of looking at the same car/engine, you might as well do the inspections yourself.
So my answer is go to the "private mechanic" but only if you see a dozen Porsches parked outside his shop and a few inside. And if he has either a PST2 or PIWIS which are expensive Porsche-specific test machines. Posession of such expensive machines is an indication that the mechanic works on enough Porsches and to a level of complexity that he has invested in the tools to do it right.
If you
are looking to save money, do some of the services yourself (anyone can
replace the air filter and cabin filter) and go to the dealer or
"private" and have them do the ones you aren't qualified to do
yourself. Or consider that some tasks can be gone by any general mechanic. An example is the replacement of an O2 sensor can be done by any exhaust shop or you could do it yourself.
There are a few things a dealer can do that an independent mechanic
specializing in water-cooled Porsches can't but not many (maybe the
dealer has the special computer that sets options and the indie
doesn't (though most Porsche-specializing mechanics at least have the basic Porsche PST2), can't really think of anything else). What a indie can do is
specialize in making the customer happy, something many Porsche dealers
have forgotten. They seem to cater to the "I have big bucks and don't
mind spending it" crowd. My mechanic charges me less in $ per hour,
will do things my way, will use used parts or parts from other sources
(but only when I ask him to), will give me a straight answer and will
tell me what I should wait on or not do. He has talked me out of more
maintenance than he has done! You won't find that straight talk in a
dealer very often.
So I save and feel very comfortable I'm not being taken. Not a bad combination.
The trick is to ask around and see who the good indies are. Not just
any foreign car specialist will do, you want one that has multiple
P-cars in his shop, maybe does a little race prep on the side, drives
one himself, advertises in the local PCA mag, etc. Then you want to go
talk to him, see his operation, discuss what you think you want done
and see how you feel about the way he treats you as a prospective
customer. I generally make this visit during the mid-day when he isn't
busy with drop-off and pick-up duties. I also let him know I'm
interested in establishing a long term relationship.
Your situation may be different. You may not have a choice. You may have a great dealer's service department in your area. But at least ask around. Stop fellow Boxster/Porsche drivers in the parking lot and ask them about their experiences.
And, if you are trying to save money, learn how to do some of the simple service items yourself. Anyone can change the air and cabin filter, for example. Oil changes save $ too. Then have the dealer or independent do the things you aren't qualified to do or don't want to do because they are too hard or too messy.