1. Calculate the volume of the rectangular prism (Can A):
The volume $V$ of a rectangular prism is given by the formula:
$$V = \text{length} \times \text{width} \times \text{height}$$
For Can A, the dimensions are $20 \times 16 \times 10$:
$$V_A = 20 \times 16 \times 10 = 3200 \, \text{cubic units}$$

2. Calculate the volume of the cylinder (Can B):
The volume $V$ of a cylinder is given by the formula:
$$V = \pi r^2 h$$
For Can B, the radius $r$ is $10$ and the height $h$ is $10$:
$$V_B = \pi \times 10^2 \times 10 = 1000\pi \, \text{cubic units}$$

3. Determine which can has the larger volume:
- The volume of Can A (rectangular prism) is $3200 \, \text{cubic units}$.
- The volume of Can B (cylinder) is $1000\pi \, \text{cubic units}$.

Since $\pi \approx 3.14159$, we can approximate the volume of Can B:
$$1000\pi \approx 1000 \times 3.14159 = 3141.59 \, \text{cubic units}$$

Comparing the two volumes:
$$3200 > 3141.59$$
Therefore, $\alpha = 3200$ and $\beta = 1000\pi$.

4. **Calculate $\alpha - \beta$:**
$$\alpha - \beta = 3200 - 1000\pi$$

Using the approximation $\pi \approx 3.14159$:
$$\alpha - \beta \approx 3200 - 3141.59 = 58.41$$

The final answer is $\boxed{3200 - 1000\pi \approx 58.41}$