Agree with lots of the above. My Samsonite(s) saw me through, very rugged and able to survive the deliberate drop from the hold at the back of a B747, (just). The strap is imperative and NOT one with a trendy plastic click-in connection, you need something with a very ordinary steel buckle that you can pull very tight.
Baggage thieves are clever. A favourite ploy is a specially sharpened motor cycle wheel spoke with which they will push out the rear hinge of a case, open case from rear just enough to feel inside for hard objects, wallets etc. etc. then re-insert hinge and pass case out, all in all takes about one minute!!! With a strong canvas strap with a buckle fastener they can't be bothered, too much time, plenty of others to go for.