The two have been aggressively competing with the high street banks and building societies, particularly when it comes to credit cards and loans. And Tesco has also now entered the current account market.
Let's take a look at what they have to offer.
Tesco Bank currently offers the top 0% on purchases credit card. The Clubcard for Purchases offers 19 months with no interest to pay on your spending. And it pays Clubcard points on your spending too. The representative APR (the annual combination of interest and charges you'll pay if you don't pay off your spending by the end of the 0% period) is 18.9%.
Meanwhile, Sainsbury's Bank offers the Nectar Purchase card, with no interest to pay on purchases for 16 months, and Nectar points on your spending. The representative APR is 16.9%.
You could also use either of the above to boost your Clubcard or Nectar points balance, even if you don't want to use the 0% purchase periods.
And if you're a Waitrose shopper, the Partnership card pays one point for every £1 you spend at Waitrose. Every 500 points you earn is worth £5 in John Lewis Partnership vouchers, which can also be spent at Waitrose. The representative APR is 16.9%.
If you're after a balance transfer, Tesco will give you 32 months with no interest to pay on your debts via its Clubcard for Balance Transfers. In return, you'll need to pay a balance transfer fee of 2.9% of your debt. The representative APR is 18.9%.
Meanwhile, Sainsbury's Nectar balance transfer card offers 31 months at 0% with a balance transfer fee of 2.89% of your debt. This card's representative APR is 18.9%.
These aren't the lengthiest 0% periods available, as Barclaycard offers 33 months on its Platinum card, with a 2.99% fee. Its representative APR is 18.9%.
If you don't need as long to pay off your debt, you could save some money. The Clubcard 25-Month Balance Transfer card offers 25 months at 0% for a 1.99% fee, which is a very strong combination. The representative APR is 18.9%.
If you only need a year, the Sainsbury's Nectar Low Balance Transfer Fee card will only charge you 0.5% for a year's reprieve from interest, which makes it the joint cheapest with Fluid. The representative APR is 18.9%.
If you don't think you can pay off your debts quickly and just want to cut your interest payments, Sainsbury's and Tesco offer the credit cards with the lowest representative APRs at 6.9% and 7.8% respectively.
Compare credit cards
Sainsbury's has just returned to the top of the best buy tables for both small-sized (£5,000-£7,499) and medium-sized (£7,500-£14,999) personal loans.
For a smaller loan, if you have a good credit rating, can repay it within three years and have a Nectar card you've used in the past six months, you could pay just 5.3% for a Shopper Loan. If you don't have or don't want a Nectar card and/or you want up to five years to repay your loan, the representative APR is 5.4%.
On medium loans, if you have the good credit rating and Nectar card and can repay in up to three years, you could pay 3.9% for a Shopper Loan. With no Nectar card and/or repaying over up to five years, the rate is 4%. However, these rates on medium loans are only available until 3pm on 22nd July.
Tesco Bank is only just behind Sainsbury's for medium-sized loans, with a rate of 4.1%.
Compare personal loans
Tesco has also recently dipped its toes into the current account market. The Tesco Bank current account offers 3% interest on balances up to £3,000, plus Clubcard points on all your debit card spending, which is pretty competitive. However, you need to deposit at least £750 a month or you'll pay a £5 monthly fee.
There are better accounts out there in terms of interest. TSB's Classic Plus account pays 5% on balances up to £2,000, so long as you pay in £500 a month. Nationwide's FlexDirect account pays 5% for the first year you have your account, so long as you pay in £1,000 a month.
And Lloyds Bank's Club Lloyds account pays 4% on balances of between £4,000 and £5,000, so long as you set up two direct debits from the account. You also need to pay in at least £1,500 a month to avoid a £5 monthly fee.
Compare current accounts