Should I close my Money-back Card and go with Tata Neu plus

FYF it is. 

decision of keeping both isn't suggestible as limit is too less.

if benefit from old one surpasses new one then keep both.

i hope you have used referral code of fellow dimers, it is beneficial for both. 

No

I heard closing the c(b)ore card and having only cobranded card, stops you from applying core cards again.

AFAIK you don't get any core HDFC card after getting a co-branded card (Tata Neu card in your case).

"Also want to know joining fee waived off or i need to pay bcz i got Moneyback card and it chrg me joining fee after 4 months later"

@U_know_Naushad can you please elaborate ? I didn't get it.

If u have ITR just provide it and ask for LE and upgrade to millennia

2 years ago I received moneyback plus card as pre-approved with a limit of 50k ,i used it extensively for 13 months but I never received any LE(it is a cursed card they say)

Finally I provided them ITR and requested them for LE  and an upgrade to millennia LTF

After few days they increased my limit to 100k and I received my millennia LTF

If it is shared then dont

my advice close all the hdfc cards at once, then if you have other bank card with higher limits then apply hdfc card again via c2c ( you can apply as soon as you got card closure confirmation).

you will get better card vairent and higher limit

After five months of using Tata Neu Plus, I felt like it is new Money Back Plus. While the 5% cashback on Tata products and 2% using the card are appealing, I’ve noticed that the rates on Amazon and Flipkart for my pin code, are comparatively low. If you’re a loyal Tata products buyer, regardless of better deals elsewhere, the Tata neu Plus is a solid choice. However, the 1% cashback on UPI transactions lacks consistency, and I’m contemplating closing my Tata Neu Plus account soon.