I am only starting out myself, but from what I can gather...
The two kinds of colormunki are quite different. Current models are colormunki display (colorimeter) and colormunki photo / design (spectrometer). These work in quite different ways, and for many display types you actually "need" both kinds of meter for accurate calibration. The reason is that the colorimeter works pretty well at low light levels, but is only calibrated against certain kinds of display (you select a profile to use, of which several are shipped with the colorimeter). For many display types you really need to create a calibration for the particular colorimeter / display combination against measurements from the spectrometer. Spectrometers don't need to be calibrated against particular display types, but don't work well at low light levels which are needed for a full calibration, and are quite slow; but as the calibration for the colorimeter is done with bright patches, they are suitable for that purpose.
My understanding is that colormunki display, despite being the same basic hardware as the i1 display Pro (often known as i1d3), is knobbled in terms of it's measurement speed (a hardwired 1s delay I think). If you are going to be reading 100's or 1000's of patches it makes quite a difference (eg generating a 3DLUT, or doing an in-depth report of your calibration), but I guess if you are just doing basic calibration it would be OK.
Colormunki display also can only be used with x-rites own SW (not suitable for home cinema calibration) or ArgyllCMS based "free" software, like the excellent HCFR colorimeter and dispcalgui. You get a bit more flexibility with the i1d3 meter as there is more support from commercial SW - though the retail supplied meters only work "officially" with some commercial SW - and need a workaround for Lightspace, for example. OEM i1d3 meters work with 3rd party SW fine without workaround, but don't work with X-rites own SW (not a big deal for HC use).
I think, all things considered, that the i1d3 meter represents better value for money. There is a place on ebay in Germany knocking out an OEM version of 13d3 meter for about £90 delivered. They are from a kit for calibrating Toshiba TVs and come in a useful aluminium carry case; but I don't know if they have been locked to Toshiba's own software and I don't know how to find out.
You should also think about how you're going to get the patterns onto the screen for testing. Using a bluray disk to play them is a pain as you keep having to change image; you can use a laptop with an HDMI output; or alternatively a Chromecast is quite a nifty way of getting the patterns on the screen if you are using HCFR or dispcalgui (or Argyll from the command line). Chromecast isn't 100% accurate, but the difference was measured by someone who knows far more than I as being imperceptible to the eye.