My 2c, i learn trad grip in the drum corp (first 7 years of playing) and we had the old slings with the drum on an angle. Marching was hell, with a dented leg and aching shoulder (this was pre the leg rest). After leaving the corp and getting my first drum kit i switched immmediately to matched (because that was what rock drummers were doing, and the jazzies using trad).
Another stint with the drum corp a few years later and the band by then had new metal shoulder carriers for the drums, but still played with trad grip.
Since having experience with both ways, i have tended to rock out on the drum kit with matched grip ,and when it comes to techy rudimental stuff on the snare (mainly rolls ) i habitually switch to trad, as i can execute them better. I am working on rudiments with matched grip and nearly on a par now so if i ever went back to the corp i would try matched.
The important thing is to ensure the stick movement is not restricted at all so the stick is used to it's full potential in all grips. There are a few other variations of grips i believe ... American, French?
The stick needs to be gripped in the same place for good balance to help control the sticks and assist evenness in playing.
I use the stick between the first index finger joint and thumb with a big gap which allows feee movement and not too strong a grip, where many drummers use second finger joint which tends to close up the gap and restrict stick movement, power loss and stress. My wrist is played in the position where it naturally falls as if picking up a cup of coffee. i.e the sticks point angled to the centre of the drum, elbow slightly pushed out. I used to play with the hands turned slightly outward i.e sticks pointed straight ahead
, but found this way gives restricts wrist movement and creats tension in the shoulders (not good). I discovered this when re organising my kit ergonomically following health probs (not drummer related).
It is worth the time to check out your grips to see what works best, unless you have been shown a good way by a tutor and you find it works well.
They are all o.k. to use, it's like everything drums, use what is the best for yourself and your situation.
Seen many pro drummers play only trad grip round the drum kit, and they cook.There are no rules.
With a good grip goes good technique and stick control(how you use it).
This one is popular these days
I found the Dom Famularo book good with a good description of grips.