I am curious which specs exactly are not as good?
Looking at the datasheet for the HP 8568, a more modern instrument would have....
Lower DANL, spurious harmonics, level accuracy uncertainty, RBW options, VBW options
And better sweep speed, number of points in sweep, timebase spectral purity and phase noise, measurement capabilities (number of markers, channel power, etc.), input protection in many cases...
And that's just looking at the surface level stuff. Look at the amplitude range on the 8568A, +30dBm to -135dBm. Even with a 10Hz RBW (instead of 1Hz with averaging to get best results), the DANL of either the Rigol or the Siglent is lower than the 8568A can even display according to specification, the sweep has many more measurement points and is still very fast, the timebase has lower phase noise, etc.
People often put old gear they grew up revering on a pedestal, and while there is some very good old gear and some old gear which is nearly as good as the top of the line stuff (I'm looking at you 8.5 digit DMMs), the vast majority of equipment has improved DRAMATICALLY from the early 80s or wherever your vintage HP bit of kit of choice is from. An entry level modern bench SA will preform better than nearly any top end system from the 80s.... and why would anyone expect differently? Now, there are service manuals available, and the build quality is good, and you're probably used to the interface if you've used them before... there are a lot of value propositions for valuing the older gear, but there is really no benefit to assuming a giant old SA is going to preform better than a newer one, especially when nothing on the datasheet suggests it.