I haven't played the Peerless but I've looked it up. I've also looked at Forsyth's website to see what Martin she would have played at 3500.
Firstly the Peerless- it's all solid wood which is good, made in Korea which is OK. The wood is mahogany including the top and it is a jumbo size. Mahogany isn't a bright topwood and its a big body so I would expect it to sound quite bassy, almost boomy. The closest Martin would be their D15.
The Martin she played it seems would be the 000-28. This is a lovely guitar and many levels better than the Peerless. It has a smaller body, with rosewood back and sides and a spruce top. It would be bell-like in comparison with clear trebles and a bright midrange. There wouldn't be the same bass as the Peerless but what there is would be tight and controlled. This is basically the same guitar Eric Clapton played on his famous MTV unplugged concert, it is that good.
So why couldn't you tell the difference? Lots of reasons. You used the word untrained and that is a large part of it. You didn't have the Peerless with you to do an A/B comparison so that makes it harder and as I said earlier, a beginner will always sound like a beginner, no matter how good the instrument.
There are also things like the larger body of the Peerless could make it sound louder than the smaller Martin (depending on how it's played) and even the room you were in.
The other thing to bear in mind is a 000-28 shouldn't really be lugged around by a young kid. It is a delicate, professional level instrument.
Martin's cheaper, laminated x series is a better option for being able to cope with the likely abuse it will get, but in my opinion the Yamahas of this world are better at producing entry (and slightly higher) level guitars
