Amity Law School, Delhi

Yes, there is. For management quota, you must appear for IP CET (of the same year when applying for management quota) and obtain a rank. Next, visit amity.edu/als where you can find the management quota form or visit the campus for one. Once you've submitted the form you shall now be selected on the basis of percentage obtained in class 12th.
There are only 30 seats reserved under management quota and the top 30 candidates shall be selected solely on the basis of class 12th percentage and not CET rank.
The list of selected students will be announced on campus (or on the website, not sure about it).
Management quota is a good option for students who scored good marks in class 12th, but could not do so in CET.
According to previous year's data, students scoring 88% were selected. So, for example, if you score more than 88% or even 85% and have a low rank let's say 4000 go for the management quota.
For more details or any other query, please feel free to ask.
Cheers.
Thank you.

Both the institutions are amongst the top 3 law colleges affiliated with IP, if you are getting both these colleges in your counseling then you can chose either one, it won't make a huge difference in sense of batch value. The one thing you should consider is convince, for example if you live in Delhi and are planning to use Public transport for your daily commute, then go for VIPS since its located in Pitampura, New Delhi.(although a new metro line is under construction for better connectivity to Amity University. But yes it's your decision).
Other things like Lifestyle, Locality, Hostel, PG's, etc. can be taken under consideration. But rest assured there isn't much difference in terms of academics, batch value, campus, etc.