Yes, since I don't have a calibrated traceable reference for rise times or pulses, I have to deduce the performance.
The simple test shows that an identical scope+probe setup produces different rise times from 2 different sources, one faster than another. Changing the probe causes a proportional change, with the sources consistent, Instek is faster than Hantek.
One can say with certainty that the RP2200, rated at 200 MHz, is faster than the Yang Sun rated at 100 MHz. But how fast they really are quantitatively, I can't say. Since the Rigol probe provides a faster rise time vs the Sun probe, this suggests that the Instek source rise time is at <= 4.8ns, it could be better, but even if it faster than 1.8ns needed to test the 200 MHz probe to its limit, I then am limited by the scope's rise time.
The question raised by the OP, is are these 'low cost' eBay probes any good?
Using the Instek rise time 4.8ns for the Rigol probe, and 6.6ns for the Sun probe, and using 0.35/rise time estimates, gives applicable bandwidth between 73MHz and 53 MHz. Since my scope is only rated to 50 MHz or slightly more, either probe is suitable to 50 MHz.
In addition to the rise time, you can also do a brute force sweep of sine wave frequency to check the -3dB limits of the probe+scope combination, and finally a qualitative appearance of a square wave distortion to complement all the measurements.
It would be good to have a reference probe and signal source traceable to a calibrated device, but I leave that task for another day.
On the sampling rate, yes, I checked each response at 1Gs/s when doing measurements, to insure I get the best results. For these photos, I combined the images mostly to avoid posting so many individual photos. I also use dot mode to confirm the scopes interpolation, and use vector to make the photos.
On the overshoot, yes, I could try to correct it, but I think it will add little more to determining whether these eBay probes are adequate for a 50 MHz DSO.
In summary, the probes don't limit the scope's performance, and the limiting step now is the scope. If a user has a fast rise time square wave source, they can easily check the performance of a no-name passive probe by simply connecting the probes directly to the signal source, and measuring its rise time on the scope its to be used on. The key is to insure it will allow the scope to perform at its rated bandwidth.
So the Rigol probe shows a faster rise time with the Instek FG, but slower with the Hantek AWG? The appears to be significant overshoot in the blue trace in the first picture, but this may also be the signal. 4.8ns shouldn't really be a hard test for these probes, it requires 70MHz or so of bandwidth, so the scope is likely to be limiting. At least in the first setup, the Rigol probe looks slightly better to me (less smooth), the opposite in the second. Note that this from a low-impedance source with a low amplitude, none are issues with Tek's current many-GHz probes, they're low-impedance inputs anyway, and won't survive a high amplitude. The scope also appears to sample too slow to really see aberrations, you should probably test one probe at a time so you can use the full 1GS/s.