As for whether Persil (and Tide) is worth buying vs. something cheaper...
I think this is very much a "your mileage varies" deal. Some people probably would find cheapest detergent good enough. Other people could get by on nothing less than a top tier detergent.
I have to admit...I was pretty cynical once about Tide, thinking that other brands were just fine. BUT my laundry needs were (and are) simple: more freshening than anything. My attitude back then might have been considerably different had I had severely stained/dirty laundry.
In recent history, I've been using Tide more often than not. I only generally need freshening, but I think Tide may work better for even that. That said...I theorize I could happily get by on some cheaper detergent if I had a different washer.
A few months back, I was using some variety of unscented All. It seemed to work OK, but I noticed a difference when I switched to Tide purclean. The difference isn't enough to make me say I'll never buy All again, but it is enough to make me say that if I can get a good deal on Tide, that's what I'll get.
I have used A&H only once in recent memory. I can't remember it very well, but I can remember not being terribly impressed. That said, I was using a sensitive skin formula. A regular variety might work better.
I've used Persil, and it worked well. I can't say if it was better than Tide. But I can say, no matter which brand has the best absolute cleaning power, that one thing I like about Tide is that it is available in unscented varieties.