I've done both. I've been through Johannesburg more times than I have fingers and toes.... I have never had a problem either way (at least with SAPS), but I can assure you, if traveling with a newbie, having the permit in hand upon arrival makes a big dent into their normal African angst. There are some other issues a "Meet and Greet" can help with discussed below.
There is plenty of information on the internet of how to download SAPS forms, fill them out, etc. You need letters of invite, form 4457 and some other stuff, of course, and if you feel comfortable (and would feel comfortable fixing an unforeseen problem at the SAPS counter), more power to you.
All that said, here are a couple of places where "Meet and Greet" come in handy:
Any airline connections that require a fast turnaround to another international flight, i.e., airlines that have no baggage agreement with each other so you have to quickly get permitted in South Africa and then tote your bags to another airline....
same thing if you're trying to catch a domestic flight with a short layover.And if your guns didn't make the cross-the-pond flight... what do you do? Travel on to wherever or have an experienced "Meet and Greet" company get your guns on the next plane when they finally arrive or do you just stay in Johannesburg and miss your connections???? .... Afton Guest House has found my bags the next day and got them on to Zimbabwe for me twice, btw.
So... If I'm staying in South Africa and being picked up by my P.H. at the airport, no "Meet and Greet", but if I have a short domestic or international connection (with no checked-through baggage service), have my wife or an inexperienced traveler with me or if I'm going to another country to hunt, I pay the money for piece of mind.
BTW, most services are in the $100 to $300 range.
Finally, I've been on Delta 200 when 70 or so guys were trying to get SAPS permits at the same time. If you are approved and your "Greeter" knows his/her business, you'll get out of SAPS in a few minutes instead of several hours (particularly when some nimrods show up with no 4457's, autoloading rifles, two guns of the same caliber, etc.)
So... I'm going back to Zimbabwe in April. I'll be met by Afton Guest House coming out of customs, will be escorted over to SAPS, they'll have my permit in hand, I'll pick up my guns without hassle, go get supper and a good night's sleep, have a eggs and bacon breakfast and talk to other African pilgrims about their hunts (done or incipient), ride Afton's van back to JNB, meet their associate/porter at the airport who'll make sure there is no hassle with SAA for the flight up to Vic Falls or with checking my guns... and be relaxing on the booze cruise by nightfall.