Some 4-way games are more picky than others.
If you give Donkey Kong any 8-way information during a game, Mario just stops wherever he is until you get back on a cardinal direction.
Other games seem to not mind it as much, and will either continue in the direction they were going, or switch directions when the diagonal is hit, depending on how they were programmed to respond to accidental 8-way info.
My current pick as a 4-way is the T-stik Plus, after you do the RandyT mod to it.
It doesn't have the huge travel of most of the other sticks (Wico, Pac-stick, Happ, etc...), and doesn't have the cloverleaf restrictor of the Nintendo and Seimitsu.
The short throw is probably why TOK doesn't think it feels like a 4-way, but I actually prefer the shorter throw because it feels more responsive to me.
Without the RandyT mod on it, the spring tension is a killer after a few games though.