Stick FUNCTION
The P-360 sticks are functionally the same as any other 8-way.
The difference between them and the other 8-ways is that they use optics to sense the stick movement, rather than switches.
The 49-way sticks are similar in operation to the P-360, in that they use optics to detect stick movement.
The difference between them and the P-360 is that they also detect DISTANCE that the stick is moved in a direction.
This makes them functionally the same as an analog stick.
For TRUE 4-way games, there really isn't any substitute for a TRUE 4-way restricted stick.
My personal preferences
Wico 8-way leafswitch sticks for games that require you to move the stick in circles.
T-stiks for games that require precise movement in 8 distinct directions.
Wico 4-way leafswitch sticks for 4-way games.
Other Sticks
I haven't used the Prodigy sticks yet, but would assume that their quality is as good as the rest of Groovy's products.
The Happ sticks I've used (Supers/Comps/Ultimates) don't feel as good to me as ALL the other sticks out there.
They are alot sloppier and springier than the other sticks.
This results in you having to move them farther when playing, and makes them twang back and forth (hitting switches back and forth as well) when you release them suddenly from full throw.
My Recommendation
Based on what I have heard you say, I would suggest going with the T-stiks.
The P-360's can't be changed from 4-way to 8-way easily, which would be a big sell point to me if I could only have two sticks.
The only hesitation I would have about the T-stiks is that they tend to hang in the corners when you are trying to do circles with the stick.
If games like that are going to be the "big" ones you play, you might want to consider Wico 8-ways, or the P-360's.
If you do go with the Wico's or P-360's, you'd probably want to add a dedicated 4-way as a third stick though.
You CAN play 4-way games with an 8-way stick, but you get dead spots in the corners where your player will either continue in the direction he was going, or just stop dead, depending on what game you are playing.