I shop at both.
A lot of it depends on the store, but this is my experience:
Fruit and veg - Tesco. They are often slightly dearer, but if you choose stuff carefully you get the quality and variety. If it's just for a basic veg soup then you can use Aldi's stuff but use it on the same day (in my experience)
Cheese - varies, but Tesco has a slight edge and has a LOT more variety. Aldi has some good stuff, though. I buy from both.
Fresh meat - Tesco is currently price matching a lot of the basics and has more variety. They also seem to take a little more care than Aldi in our local stores.
Frozen - Not really tried much in Aldi. Their frozen chicken portions were fine, but they didn't have low fat mince and the free from stuff isn't there.
Cooked/sandwich meat, esp salami - Aldi, much nicer and less expensive
Chocolates and biscuits - Aldi
Crisps and snacks - Aldi, just as nice and much less expensive.
Jars and tins - Aldi is less expensive and their curry and pasta sauces are great, but they don't have the range if you want a variety of stuff. Their sweetcorn isn't as good.
Pasta - can't really judge much as we have to have gluten free pasta but some of the household are fine with regular stuff and the Aldi own brand pot noodles are okay and less expensive.
Coffee (only DH drinks) - Tesco (most people prefer Aldi)
Baking stuff - Tesco. Aldi doesn't have the variety
Free From stuff (gazillion food issues in this house) - Tesco. Aldi is very limited.
Bread - Morrisons or Lidl (I shop everywhere) but Tesco slight advantage for variety, Aldi better for the fancier stuff. The prices are slightly cheaper at Aldi
Cleaning - Astonish stuff from local shops or Amazon.
If you have a clubcard for Tesco and use it carefully (don't buy stuff just because it's marked down but because you are going to use it) then there are some decent deals and yesterday there were signs everywhere about them price matching with Aldi. You also get points.
My opinion, for the stuff we buy in our household and way we work, on the whole, by and large, all things considered, Tesco is a little more expensive than Aldi, but not much, with greater variety and some items better quality. It is worth, however, dipping into Aldi for some of the other stuff on the regular, though.
Some people have stamp collecting or hiking as their hobbies. I have grocery shopping.