I teach ancient style snare on old rope drums, so we only do traditional. I can't comment on the pros and cons of each for lefties, but I have noticed that they pick up the traditional grip more easily than righties. Last night I had a first lesson with a pair of twins, one righty and one lefty. It was obvious the lefty "got" the grip much more quickly than his brother.
It seems that after that initial moment, the challenges are pretty similar - retrograde motion is just as difficult, bouncing seems to depend on the student more than the dominant hand, stick control just takes time.
I would suggest that unless you're playing on a sloped head, the difference in power between the hands probably won't be resolved by changing grip. The best thing is to play your most basic rudiments (start really basic - singles and long roll) with your eyes closed and really listen for evenness at every speed. Then record yourself playing them and listen. Do daily for a couple weeks and it will probably clear up.
/* What follows worked for me, and I'm pretty sure that it's not a good idea. The concept could probably be applied in a safer way. I have not used this method with any of my students, but I believe the concept is sound: balance the hands by building hand strength independently. Below the picture you can see exercises I use with my own students. */
I really struggled getting my left hand to perform well, my wrist was really stiff and tired easily. My instructor installed an old rusty socket on a stick for my left hand, along the lines of one of these. When I switched back to my regular sticks a few weeks later, my stamina (and flamacue) was immensely improved. I've never done this with any of my students, as I'm concerned about repetitive stress injuries (RSIs), but it certainly worked very well in my case. He later also made each of us a "stick" from 1/2 inch steel dowel (smooth, not rebar) for stamina building, 500 on a hand. I still use it periodically for a workout.
If you determine that the problem is either strength or stamina, here are some exercises I use:
- Use different weight sticks (probably heavier) for a week. The change seems to reset the autopilot and help players focus on sound and feeling.
- Play on a pillow. This builds wrist strength since there's no rebound. A bowl of water also works well but it potentially messy.
- All on one hand, either bucks (soft LOUD soft LOUD) or just straight beats, at a steady tempo (140-180bpm) for either a time limit (3 minutes) or a number (600), depending on age.
- Old style long roll (pre-1850s), where the second stroke on each hand (rebound) is accented.
- Roll as fast as possible (cleanly) without bouncing.
- In all cases, daily practice is necessary to be most effective.
Then, once the hands are stronger than they "need" to be for general playing, focus on listening to balance the hands. Eventually this will become second nature.
- Use two different style sticks and make them sound as even as possible. Perfection won't be possible, but the exercise helps to focus on the problem.
- Close eyes and play simple rudiments while focusing only on sound. The teacher can make a sound (click for example) when they can identify the hand that is playing without looking.
- Record rudiments and listen to yourself.
- Play on something that isn't a drum, like a countertop, and try to even the sticks.
- All these should be done slower than normal and on a pad, not a drum.