Priority tags mean nothing to be honest. So many people travelling in ET, WT or WT+ leave them on from previous flights that they're not used to indicate which cabin you're in and whether your bags should be priority delivered. They're not called "snob tags" for nothing!!

The tag with the destination and bar code is the one which indicates whether your bag is priority or not. If you're in CE, CW, or F the loading team will be able to tell from this tag and load your bag accordingly. Were you travelling in CE or ET? If CE your bag should have been priority sorted through the barcoded tag. If in ET and relying on the orange priority tag, that will mean nothing and your bag will come up with all the other ET bags.

However, on my recent trip my bags were within the first 10 on the belt (after the golf clubs!!) and arrived at the baggage belt at LHR a few seconds before I did. They were also in the first batch of bags to come out at my destination. I was in CW so can assure you the system works the vast majority of the time.