1

Warning: I don't know either language.

The alphabet is basically the same; a few characters (e.g. there are three kinds of r in Kurdish) are different.

I wouldn't expect much mutual intelligiblity based on this sample text from omniglot.com:

Kurdish:
Hemû mirov azad û di weqar û mafan de wekhev tên dinyayê. Ew xwedî hiş û şuûr in û divê li hember hev bi zihniyeteke bratiyê bilivin.

Persian:
Tamâm-e afrâd-e bašar âzâd be donyâ miâyand va az lehâz-e heysiyat-o hoquq bâ ham barâbar-and. Hame dârâ-ye aql-o vejdân mibâšand va bâyad nesbat be yekdigar bâ ruh-e barâdari raftâr konand.

Translation
All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.

(Article 1 of the Universal Declaration of Human Rights)

dinyaye and donya are loan words from Arabic (=world) and I expect both languages have a lot of such borrowings, which might help a little if you were to study Persian after Kurdish or vice versa.

2

According to the language family tree shown on the Wikipedia page on Iranian languages, http://en.wikipedia.org/wiki/Iranian_languages the branch including Kurmanji broke off from the branch including Farsi at or before the time when Parthian and Median became separate from Old Persian, ie before 700BC. (Pashto, Ossetian, etc separated still earlier.)

Languages that separated as little as 1000-1500 years ago (eg Slavic, Romance) have relatively little mutual intelligibility despite their similarity on the page, so to expect any when the split was at around 3000 years ago is clearly well beyond hope.

Curiously, Kurmanji is more closely related to Balochi than to Farsi.

3

Vinny, although I second what you say on the alphabet, the excerpt you are showing is Kurmandji Kurdish though, not Sorani.

I have studied both Persian and Kurmandji Kurdish.

Some basic words are the same - sard, germ, dur, nazdik and others.
The grammars ressemble each other a lot, with sentence structure, and the use of the Ezafe. However Kurmandji Kurdish is more complicated. It uses grammatical genders, and in the past tense it uses the Ergative, something that Persian does not use.

Maybe someone else who has done some Sorani will show up. Would love to hear from someone who can say something about Baloochi and Kurdish, but that is a long shot.

4

Sorry cannot edit - because Kurdish is a little written language, both dialects of Kurdish vary within a continuum. Every one knows Howramani is "from a different world". The Kurdish of Kermanshah on the other hand is said to be a lot closer to standard Persian than the Kurdish of Sanandaj.
At the same time I have heard Persians on holiday in Kermanshah complain that the local market sellers only spoke Kurdish, and did not understand what they were asking.

As for my own experience o learning tidbits of Sorani - most of the basic words i was taught in Sanandaj by locals ressembled neither Persian nor Kurmanji!