In terms of the traditional performance measures of a spectrum analyser (input IP3 and IP2, input VSWR, phase noise, overall measurement uncertainty and spurious free dynamic range) there is only one winner despite the >25 year age gap. The 8560E is going to easily outperform the Siglent analyser in this respect.
However, the Siglent analyser offers lots of modern features and it also has a digital IF and a really nice and large display screen.
The digital IF will offer much improved log accuracy compared to the older 8560E when the 8560E is used on wider RBW settings. The 8560E only offers digital RBW on the narrower RBW settings.
I've only used the TG with the A version of the HP 8560 and it was fairly grim to use. The tracking performance is not great because the tracking gen source is not accurately locked to the rest of the analyser's synthesiser. So it can drift and cause tracking errors on narrow RBW settings. Maybe the TG with the 8560E is better?
Many people will prefer (and be happier with) the Siglent analyser, especially if the aim is to use the tracking generator a lot on narrow span settings.
So it really is up to you to decide which is best for you.