Two different players.
Quinn is very agile, good with the ball at his feet and generally tidy. He's a great player to have when you need to keep possession, and as mentioned seems to link very well with wingbacks on the left. He also uses that agility to harrass opposing players when they have the ball, keeping pressure on them rather than lunging in with tackles (for the most part). He doesn't tend to shoot much though, more twisting and turning before laying the ball off for others.
Meyler usually has a big engine and can run himself into the ground. As with Quinn he tends to close players down quickly but where Quinn usually maintains pressure Meyler likes to stick a foot in, which can win us the ball or can give away free kicks. I wouldn't say he's as comfortable on the ball as Quinn - he can't keep it glued to his feet as easily and his passing isn't as crisp - but he does give a bit more of a direct threat, being not too bad in the air and actually has a pretty good shot on him. Some of our wins last season came from Meyler running past our forwards and getting in the box.
The situation has changed massively for Quinn this past week or so. When Long was here and Snodgrass fit he seemed nowhere near the team, and even behind Boyd. Now two players are out of the equation, and Ince/Aluko are being used more up front rather than in midfield, there's suddenly an opportunity and he's grabbed it well. Quinn has looked lively, Boyd has looked off the pace and rusty.
I'd say for both Quinn and Meyler their best position is in the 'Snodgrass role' ahead of Livermore and Huddlestone in a central midfield three. Quinn to link up with the wingbacks more and bring them into play, along with his ability to maintain possession, and Meyler to be more of a direct threat. Which of the two plays will probably depend on fitness, form and how Bruce feels the opposition will line up. On performances so far this season Boyd should be behind the two of them for that role. Of course, a new forward signing would likely see Ince drop back there and make it tougher for Quinn to get a start.