Yes, the aperture difference affects diffraction, but in practice the real-world difference is likely small. A pinhole at f/206 produces a smaller diffraction blur than one at f/290, so the Titan should have a slight theoretical sharpness advantage and slightly less wavelength-dependent blur. The tradeoff is shorter exposure times at f/206, while the slower f/290 can be easier to time by hand for long exposures.

With pinhole cameras, though, image quality is dominated by whether the pinhole size is well matched to the focal length and how precisely the pinhole is made. If both cameras use well-made, optimized pinholes, the difference in sharpness will probably be minor. Film choice also matters: if the film grain is as large as or larger than the diffraction blur, you may not see much difference at all.

So: f/206 should be a bit less diffraction-limited than f/290, but both should perform well, and manufacturing quality, optimization, and film grain are likely to matter as much or more than the f-number difference itself.