Are budget tires from Aldi or Lidl really that bad?

I wouldn't write them off completely, but I also wouldn't use them as everyday tires for your regular driving. Budget tires from discount stores often aren't badly designed, but they wear out noticeably faster than name brands and wet grip is usually weaker - you'll notice the difference when it rains or the roads are wet. If you drive a lot or care about safety, it's worth investing in better tires, but for occasional city driving, the discount store ones will do the job.