If a gun is part of a pair or matched set, would that indicate better then average quality?

The gun is question is #2 a J. Burrow hammer gun with a Jones underlever. I don't currently have pictures of it.

Your assumption is usually correct. Only the wealthy could afford to shoot where pairs were required and they did not generally buy poor quality guns. However exceptions must exist!
A work of caution, it costs little to engrave a number '1' or '2' on a gun, gold inlay is not that much more, so this might be a clever way of raising the perceived quality (and price) of an ordinary gun.
Unless of course you have seen its mate and can confirm that they are effectively identical.

It depends i think, i have seen some pretty ordinary Anson and Deeley boxlocks in pairs or part of a pair. My own gun is no.2 of a pair, while it has nice engraving and wood, underneath its still a fairly standard A&D boxlock.

I also have a sidelock non-ejector thats one of a pair, you would imagine for guns meant for driven shooting, ejectors would be a must.

I would expect that a pair were made identical. However just yesterday I was discussing this with a well known gunsmith who told me that he has seen pairs that look exactly alike on the outside but were vastly different on the inside suggesting the receivers were sourced from two different suppliers. I suppose that could happen but it does seem odd to me.

I have no idea where it's mate might be, since it isn't, as far as I can tell, a prominent maker, maybe I just got lucky. I'm just curious, I like the gun and that's what matters.

Not all guns marked #2 are part of a true or composed pair. It was explained to me that a frugal shooter would have his gun marked with the number 2 and tell his friends that number 1 was back to his gunsmith for repairs. I concluded if a pair was needed he would then borrow a second gun. And unless you are shooting driven birds a pair is more for show than anything else.

There's generally a premium for a matched pair in Europe. In the States, because only the relatively few people who might travel to shoot driven birds would have need for a matched pair, you can sometimes pick up a pair for less than you'd pay for two individual guns of the same make and model.

I've owned a couple matched pairs. First pair were Army & Navy 12ga boxlocks made by Webley & Scott. Not particularly fancy, but there was some interesting history behind them. I had the original owner's motor case. Turned out he was a British brigadier (like US brigadier general) and WWI veteran. The nice thing about a pair is if something goes wrong with #1 when you're shooting birds over dogs here on this side of the pond, you have an identical mate as a backup. The only modification I did to mine was some minor choke surgery. I left #2 with a tighter left barrel, and that was my later season ringneck gun.

I think as a general rule, matched pairs are a step above. I own a pair of English BLE guns. The stocks obviously came from the same tree and barrels are of chopper lump construction. Very high quality boxlock guns. And, way too nice for me to hunt.

Chantry, associating a specific (higher in this case) Original Quality grade (OQ) with paired guns falls into the same buying trap as does trying to associate specific quality grade with a maker's name. Paired guns are usually in the higher OQ's just as most Purdey's are best work sidelock ejectors. But not all in both cases. The trick here is to educate yourself sufficiently to be able to identify the Original Quality grade independent of maker or paring or provenience. A best work gun is just that. A farmer grade gun is just that.

DDA

Chantry, a further example of pairs not being "best" quality of a gunmaker's art is my H. Atkin 12 gauge which according to Atkin, Grant and Lang is #2 of a pair made in 1938. The action appears to be by W&S, a BLE, but with simple border engraving and non-fancy grade wood. It is well made, but simple in design and execution. Gil

As explained to me by a London maker's manager, the "matched" part was so as to make two totally identical guns in balance, feel and tactile sense that the user would not be able to know which of the two he was shooting. The idea being that no perceptible difference in the guns would be allowed to ruin concentration during a drive.

To get that kind of identical feel takes skill and time so a gun from a true pair is likely to have had more work lavished on it.

I wonder whether favoring one of a pair and using it more changed its tactile sense in the hands (due to more wear), and thus ruined the matching that was the original goal.

Gil, my A&N pair, also by W&S, were only slightly fancier than that. What it comes down to, especially with vintage British pairs, is that there were people who were likely to be invited to the occasional driven shoot (which were almost entirely non-commercial back in the day) and who wanted to have a proper pair for those occasions. But they didn't necessarily do a lot of driven shooting and, while relatively well off financially, didn't have the disposable income to drop on a pair of best guns. And perhaps, if they were interested in impressing their fellow shooters with anything, maybe it was their ability with the guns in question rather than how much those guns cost.