Mechanical Engineering

Mostly, people tend to do engineering after Diploma.
That is what even I suggest you. Gone are those days when people used to consider engineering as an ultimate degree.
Engineering is now a basic degree for any job.
Even if you get placed with your Diploma, I suggest you to complete engineering and join any job.
If you have engineering with Diploma, you are considered to be technically sound.
So, go for engineering.
Just in case, you end up joining any company after Diploma i.e without an engineering degree, I suggest you to do some certification courses in the field of mechanical engineering meanwhile to enhance your knowledge before joining engineering.

Now, assuming you want to know about engineering colleges, for this case comparison between BVM and LD.
This is an answer from a BVMite, still, I will try to be neutral.
1. For me, BVM is better than LD in terms of education offered. BVM has the most experienced and knowledgeable faculty. LD, on the other hand, is not so famous for its education. Lectures are not taken as per schedule, attendance is never an issue in LD.
2. Looking placement wise, more companies visit LD in comparison with BVM, but if you are good enough and have good grades and aptitude, you will get placed from both the colleges.
3. The campus of LD is very big in comparison with BVM, but the infrastructure of both the colleges is very old. BVM has all necessary facilities for students.
4. If you want to live in a city and experience city life then go for LD and if you want to live in a peaceful city with all necessary infrastructure then BVM is a good option.
Overall, I would suggest BVM.