Allen's study packages are better than Aakash's study packages for the following reasons:

1) Allen's physics is more interesting and they have given tips and tricks for solving problems faster. There are more solved questions and past paper questions so you get more practice. 

2) Allen's chemistry is better as they give explanations for concepts and reactions, and only material relevant for NEET is mentioned. There are plenty of solved examples.

Allen's biology is long and tiresome to read, but if you make your own notes from their material, you will do well. Aakash's biology is better. Allen biology gives plenty of past AIIMS questions for practice.

Overall, Allen's packages are the best, but you might have to use Aakash for Biology. In Aakash classes they explain things very well, they have good faculty, so the classes are quite helpful also. 

Hope this helps! Good Luck!

Yes, they are effective if you will utilise it properly...