This is what I learnt online. I've never been to Andamans, but planning to go in March for a Scuba course.
Neil and Havelock are both great places.
Havelock has better facilities and is a bigger island. The beach #7 is supposed to be the best in Asia. Of course,this also means lots of tourists.
I understand that the best dive schools in Havelock are DiveIndia and Barefoot Scuba. Both of them have great reviews. DiveIndia is the oldest DiveSchool in Andamans and their divers have discovered most of the top dive sites around havelock.
DiveIndia has now opened shop in Neil too. There is one more small dive school called IndiaScubaExplorers.com (run by Johann - 09474238646). My friend has dived with these guys and she recommends them highly.
Neil is much more laid back as compared to Havelock (but really havelock is pretty slow), you probably will get a better Instructor to Student ratio because most people go to Havelock. For a beginner, that's good.
Neil also has lots of new dive sites, and people have just started explorining the area. You will be one of the first few to do so along with the dive centers.
You will not go wrong with either option.Andamans are supposed to very beautiful. I personally would probably go for Havelock, because my wife is a non diver and she may a few more things to do in Havelock (but not many)
http://www.indiamike.com/india/andaman-and-nicobar-islands-f41/
http://www.scubaboard.com/forums/general-asia/405903-andaman-islands-diving-havelock-neill-better.html
http://www.diveandamans.com/
http://diveindia.com/
http://www.indiascubaexplorers.com/
Check out the facebook pages for DiveIndia and Barefootscuba and India scuba exploreres.
You can contact me at keshavram AT gmail DOT com