Which is greater? a rise of 1 degree Fahrenheit, or a rise of 1 degree Celsius?

One-degree Celsius is greater than one degree Fahrenheit.

The relationship between them can be shown below:

[°F] = [°C] × 9⁄5 + 32 (Fahrenheit to Celsis Formula)

So, for temperature C1, we get:

F1 = C1 × 9⁄5 + 32 (eq. 1)

For another temperature let's say C2, we get:

F2 = C2 × 9⁄5 + 32 (eq. 2)

Subtracting eq. 1 from eq. 2, we get

F2- F1 = C2 × 9⁄5 + 32 - (C1 × 9⁄5 + 32), or

F2 - F1 = C2 × 9⁄5 - C1× 9⁄5 + 32 - 32, or

F2 - F1 = 9⁄5 × (C2 - C1), or

delta F = 9⁄5 × delta C, or

delta F = 1.8 × delta C, or

ΔF= 1.8 × ΔC

So, for each variation of one degree on the Celsius scale will correspond to a variation of 1.8 degrees on the Fahrenheit scale.

This meas that 1 degree Celsius is greater (represents a greater variation) than 1 degree Fahrenheit.

For a given temperature, the value in Fahrenheit will always be greater than the value in Celsius. This, though, doesn't necessarily mean a hotter temperature. You can easily see this behavior on a Celsius to Fahrenheit conversion table.