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Press versus drag
A rocker is a long curved blade you press straight down while rocking it across the pizza. The cutting force is vertical, the blade barely moves horizontally, and a 14-inch rocker crosses a 14-inch pizza in one press.
A wheel is a rolling disc you push along. The cutting force is a combination of downward pressure and forward motion, and the blade travels the whole length of the cut.
Every difference below comes out of that one distinction.
The comparison
Rocker
Wheel
Cutting motion
Vertical press
Horizontal drag
Topping displacement
Minimal - nothing pushes along the cut
Real - toppings pile at the far edge
Passes per cut
One press
One to three, depending on the crust
Thick crust
Good, if the blade is long enough
Stalls unless the wheel is 4 inches or more
Effect on the surface below
Presses the full blade length into it
Drags a hardened edge across it
Storage
14 inches, needs a sheath
Fits a drawer
Cleaning
A single flat blade, easy
The axle traps cheese
Safe on a stone
No
No
One press
What a full-length rocker buys you
A 14-inch blade crosses a 14-inch pizza in a single movement, so nothing gets dragged and nothing needs a second pass. That is the whole argument, and it is a good one.
Where each one wins
Rocker. Heavily topped pizza, where drag would rearrange everything. Thick crust, where a wheel stalls. Anyone cutting on a board and with somewhere to store 14 inches of blade.
Wheel. Thin, lightly topped pizza. Small kitchens. Non-round shapes and trimming, where a long straight blade is the wrong tool. And it is the cheaper option by a long way.
Neither, if you cut on the stone. Both press or drag hardened steel into the surface. A wheel leaves gray metal marks on cordierite; a rocker will take seasoning off a steel in a line. Scissors with a spatula base are the answer there, or move the pizza to a board.
Fourteen inches of exposed blade needs a sheath and somewhere to live. That is the practical objection to a rocker, and it is a real one.
The size rule for each
Rocker: at least as long as the pizza is wide, or you lose the single-press advantage and are back to overlapping cuts.
Wheel: at least 4 inches in diameter. A smaller wheel has a steeper approach angle, so it pushes the crust ahead of itself rather than cutting into it - which is why cheap small wheels feel blunt even when they are sharp.
The third option
Scissors with a spatula base cut with a shearing action and keep the blade off the surface entirely. They are the only one of the three we would use on a stone, and they are slower on a thick base. Full ranking in the cutter roundup.
What we did not do
We have not baked on any of these. Every guide in this category says it tested a dozen stones; we would rather say plainly that we did not. What we did instead is on this page in full: published specs with their sources, thermal arithmetic from material constants with the working shown, and the makers' own manuals read rather than paraphrased.
The picks
What we would buy
Checkered Chef
Checkered Chef 14-Inch Rocker Pizza Cutter
Fourteen inches of blade cuts a 14-inch pizza in one press, which is the only real argument for a rocker. It also means 14 inches of blade pressing straight down onto whatever the pizza is sitting on.
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OXO
OXO Good Grips 4-Inch Pizza Wheel
A big wheel with a thumb guard. The cheapest competent cutter here, and the one most likely to drag a hardened edge across a surface you did not want marked.
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Dreamfarm
Dreamfarm Scizza Pizza Scissors
Scissors with a spatula base, so the blade never touches the surface underneath. On a stone or a seasoned steel, that is the whole argument - a wheel drags across the surface, and this does not.
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Questions
Frequently asked
Is a rocker pizza cutter better than a wheel?+
For heavily topped or thick pizza cut on a board, yes - one press per cut and nothing gets dragged. A wheel is cheaper, stores better and handles trimming and odd shapes. Neither belongs on a stone.
What size rocker pizza cutter do I need?+
At least as long as your pizza is wide. A 14-inch blade crosses a 14-inch pizza in one press; anything shorter means overlapping cuts and you have lost the point of it.
Why does my pizza cutter drag the toppings off?+
Because a wheel cuts by moving horizontally, so anything it does not slice cleanly gets pushed ahead of it. A larger wheel helps; a rocker or scissors avoids it entirely.
Can I use a rocker cutter on a baking steel?+
Not without marking it. A rocker presses its full length into the surface, which will take seasoning off in a line. Move the pizza to a board first.
Sources
Every number on this page came from one of these, or from arithmetic on one of these that we showed in full.