Theres some good stuff in this thread re machine polishing.
I think the advice to stay away from rotary (angle grinder) polishing is sound unless you have access to some tuition or are prepared to go to the scrappie and buy some panels off of a car that is the same model as yours to practice on.
Swirling is almost certain if going down the DIY rotary/angle grinder route unless you have a good technique and the right polish/pad combination. The key thing with roatry polishing is speed control and it is this that makes most angle grinders unsuitable for polishing work. Rotary polishers are designed to have variable speeds, soft start and in some cases load sensors to ensure that speed does not diminish with pressure applied to the polisher when working.
Different paints generally react differently to different paint types so in this case the original manufacturer paint will probably need a fairly aggresive compound such as Menzerna Power Gloss of Pro line Intensive polish followed by something like Menzerna final finishing polish or maybe Poorboys World SSR1, where as the new paint probably will not need anything more than say the PB World SSR1 or Sonus SFX2. For the absolute best results one brand or grade of compound is generally not enough!
The random orbital machines such as the Porter cable, UDM and Megs G220 are good machines and are much less likely to inflict damage on paintwork if used correctly.
If I have read the posts correctly there are two problems here?
1. The new paintwork does not completely match the old paintwork due to the ageing of the old paintwork?
2. The car has some swirling which needs to be removed?
A1 To be honest I don't think any amount of machining will rectify the difference in colours and if it was me I would take the car back and ask for a correct match.
A2 In relation to the swirling you could either go down the machine polishing route or try using a polish which is designed to remove or hide swirling.
This product from Duragloss is a good product and I have used it to hide some pretty horrible swirling and micro scratching
http://www.duragloss.co.uk/sb-products.asp?productid=2322&category=86This should probably be topped off with a good finishing sealant such as this one (again from Duragloss)
http://www.duragloss.co.uk/sb-products.asp?productid=2325&category=86Good quality waxes are also quite good for hiding minor imperfections, but if you go down this route try and make sure that you use a wax with a high percentage of pure carnauba.
If going down the Pro route, a MK4 with light to moderate swirling would probably take about 3-4 hours to complete the machining, in addition to this the car will need washing and claying prior to machining and then need finishing off with a good finishing product once machining is finished. So I would reckon 5-7 hours work if paying a pro to complete the work.
I'm quite happy to talk anyone through the possible solutions (DIY or paying someone to do the work) just give me a buzz (numbers are on the web site using link below) or PM me