Hello and welcome to GTP Dave ^^, you've already met our drifting vetran/professional Silvia-Drifter whom is right about mixint tires. Go to a thread titled 'who cares about sim tires!' thru all of it, trust me and what SD said. Mixing tires is not so a great idea, even for 4WD, hell, for all the drivetrains it's not. Go to the said thread to get all I mean since I don't think I (or anyone else would) want to go thru why mixing tires is bad (again).
Besides that, welcome and I hope you enjoy yourself here.
I use the Dual Shock as well, but I use a stick for steering while I use the buttons for acceleration and brake. I can drift preaty well with that setup, then again I lack a video capture card so my words may just sound like bull...I wish I did have one...

...anywho...
If you want to know also, my drift cars are a Corvette Z06, 438bhp, sims all around with just about every other mod save for anything permenant (port polish, lightweight tunning etc...) and a 460bhp Grand Sport Corvette, also on sims with similar modifctions, and also an 86 Trueno with either 203 or 245 bhp depending if I use NA or Turbo Stage 2 kits.
It's possible to drift well without mixing tires, it takes time, technique and some degree if not a total degree of balance to get everything right to even start learnning how to drift a car.
A good, but rather painfull (depends if you're willing to swallow your pride for a short while or not and you may or may not understand why in a short instance...) process is to learn how to send your cars into drifts with NO changes, ONLY sims, even for the 600bhp cars, then again you could aruge to use stronger tires but it really depends.
To look at sims one way, they are the lowest griping tires possible and maybe even the worst that teach you vauble driving techniques in different directions. To another, they don't call them simulation tires for NO reason, they are to simulate as closely as the developers could at the time the behavior of the car. It's argueable just how sims work on EVERY car, an example is the Opel Astra, or at least the one I tuned, I put on sims and I had a very...difficult time trying to keep the car in a strait line, I sware it was my setup and I may try it again someday... but the thing to argue for blanace is not only power but weight as well. The Opel Astra Touring car is preaty light with 450bhp standard, and becuase its a race car, of course you need to drive it a lot of the time on racing tires. Other cars like the Z06 Corvette with 385bhp may be heavy at just over 3100lbs (but so is an EVO VII and maybe the VIII...) but considering its in the same class as a Ferrari 360 and even a 911 Turbo (996 model) its actually the lightweight of its class (unless you count an AE86 Trueno from a certain Anime or an R34 GTR...). To think about it, it is a lightweight even for its weight and it a very good car to drift with...easy as hell to spinout with if youre not carefull but fun also if you know what youre doing.
It really depends on just about everything setup in a car, tires included. Some cars have good balance with Sims, others may not, it depends really.
But it is good pratice to drift with a lot of normal cars, either go to arcade moode and go for drift settings or buy a normal car, slap on sims, make sure ASM and TCS are OFF (otherwise youll be wondering just why you cant pull your car into a sustained oversteer...and youll get fustrated...) and there are a few good starter cars inlcuding the FD3S RX-7 (latest model), AE86 Toyota Sprinter Trueno, Nissan Silvia S13, Corvette Z06 or even a Camaro Z28 (yes, even a 3500lbs 285 bhp 324lb-ft car...). In time, you'll be preaty good, then again I have yet to see anything from ya so I can't really say just what skill level you are at (then again you use mixed tires or at least on that Subaru...but what in the heck to do I know anyway?)...a key to getting better is to just pratice on a good base I suppose...
Maybe I should have just stuck to the simple intorductions...bah...again welcome to GTP and I hope you have a good time here.