I can only speak from the perspective of a 14 x 5.5 DW Collectors maple snare compared to a Tama Artwood 13 x 7 maple snare.
Though they are different brands and ply thickness (6 ply for the DW, 7 ply for the Tama) I used the same batter heads and snare wires (Evans HD Dry + Puresound Custom Pro wires)
IMO, the dimensions used by each drum has a specific purpose and objective. It would be extremely difficult (at least for me) to synchronize these 2 dimensions to get the same tone.
The Tama has a unique higher "pop" to it. That is why I ordered that size. I also have a Pacific Blackout 6 x10 popcorn snare whose dimensions are specific to a type of tone (brighter "pop" - such the name)
The 14" has a deeper, fatter tone that I would have a hard time converting to a pop unique to a 13 x 7 snare.
I like both tones, so I get them both and switch between them. My 6 x10 is an awesome side snare with a fricken mean pop to it. I got that drum free with my Zildjian A Custom cymbal set last Black Friday, but all my drumming buddies say it sounds the best.
It's like comparing apples to oranges IMO.