Here's one thing to keep in mind when trying to "duplicate" someone else's sound. What you're hearing is a recorded, processed snare sound....thru a speaker. You're gonna try to duplicate a sound that is "not the actual acoustic" sound of that drum. The room the drum was recorded in has a big effect on the overall sound. I've had drums sound great to my ear...and then hear them on playback...sounding like garbage. And also the reverse. Drums sounding like garbage in front of me...and excellent on playback.
I'm old school(very old school!) and I use to try to get my snare to sound like Nigel Ollson, Elton John's drummer. He had a deep sound that was actually fairly easy to duplicate just by putting a music book on my drum. Nowadays, you have all kinds of electronics that make the process even easier and more fun play with until you get it exactly the way you want.
Get a Roland brain and use triggers on your drums.
As a sound engineer and a drummer myself i can safely say that duplicating a sound is very difficult and damn near impossible. Your best bet is to figure out what sound you want and go from there. Developing you own sound is always a better bet than trying to copy someone else. Besides there is no originality in that right? Unless you are in a cover or tribute band. You will never duplicate a recorded sound that has been processed through a studio unless you know exactly every step of the chain and every device that was used to record any instrument. Even when i record....unless i do it 100% exactly the same as the previous time it is going to sound different to the trained ear. When you listen to any one of your favorite groups...listen to a few of their albums. They WILL differ slightly if not completely from album to album. There are just too many variables!
Me personally like my snare to be able to get out as many dynamic characteristics as possible with my snare. Try a variation of this set up and I think you may like it. This setup below will generally give you a clean solid crisp center hit with out allot of ringing or over tones. Dynamics out site of the center and a nice pingy ring and the edge. granted getting these different sounds out of your snare will also depend on playing technique.
SHELL: Your Choice depending on how much you want you snare to project and/or resonate this is also determined by the heads and their tension.
RESONATE HEAD: Evans Clear/ Medium Tightness (tap the head at each lug while tightening, you will want this head at least 1/2 the pitch lower as you expect to
out of your batter head. All points around the rim of the drum should be pitch matched. Your Resonant Head
'bottom head' is the head you will want to adjust to get the depth or pitch you want.)
BATTER HEAD: Evans Reversed Power Dot Center 2ply (tap the head at each lug while tightening, you will want this to be significantly tighter than your resonant
head. The top head is key in order for dynamics will work. All points around the rim of the drum should
be pitch matched. The batter head is what will give you your stick response. The tighter it is while
accounting for your desired pitch will give your more stick response and natural stick bounce reducing
any fatigue while playing. It may take some getting used to if you like playing a very deep loose batter
head but once you adjust...rudiments and dynamic ability will feel better.