My opinion.
For first timers or recent/new CC holders, it really doesn't matter - whether it is
a core card or a co-branded card. What they need is a CC to meet specific needs - fuel, shopping, grocesies, services or casback. If such a card comes with LTF benefit - nothing more to ask - for such users. Forget about whether it is core or not - if it meets your needs - take it. And, these users have little choices to make - low CIBIL scores, low limits on the 1 or 2 CCs they hold.
For CC users who are 2-3 years experienced, held 2-3 cards or so, and know the in-n-outs of the CCs, there are many options available. By now, these users must have built a good CIBIL score, got 1 or 2 limit enhancements and know the rules of the game n the tricks to apply. There woukd be many choices of good cards, special n premium cards. They can afford dump cards n get better replacements in a flash. The core n non-core cards start making a differenve to them - or so they think - and act accordingly.
I am told that HDFC is a different ball game altogether. I see no reason why you should not take a Tata Neu card - it is a good RuPay card - if your area is serviced by BigBasket. Forget about HDFC Core cards. There are many optipns available for normal users. You may not miss much.
All that percieved benefits are only for those who spend on those parameters.
Focus on what, where n how much you spend and take a CC (1 or more) which maximize benefits for your type of spending. Forget what X, Y or Z got so-n-so top end card... Their spending pattern demands such a card. Your's may not.
Know that basic rule and get going. You will never be unhappy.