Complicated or advanced? The hellenistic period was arguably a huge explosion in terms of math, architecture, medicine, and early material sciences (think greek fire). I'm happy to expand on any of these with sources.

In terms of complication, the antikythera mechanism is, without a doubt, more complicated than most machines found from the era. I suspect there are more calendar-oriented discoveries to be made, but I'd also like to offer simple machines in themselves. Yes, they've been around forever in various forms, but the principle of mechanical advantage and interlocking mechanisms tuned to mathematical ratios that underlies the antikythera mechanism was hugely influential across all greek technologies: think the astrolabe, the aeropile (not really used for anything, but definitely a steam engine), levers, water mills, pumps, canal technologies, plumbing, centralized water, etc. You can easily extend this into roman times without much interruption: key stones, aqueducts, cement, siege weapons, etc.

The antikythera mechanism IS complex, yes, but it's more interesting by virtue of being a computer: that is, it takes inputs and produces outputs, instead of performing some mechanical function directly. It has no use except for calculating the date, which is pretty unique in ancient times. I would probably put the astrolabe and surveying tools at second to antikythera mechanisms in terms of impressive technology, and the rest of the simple-machines (pumps, cranes, winches) in terms of mechanical complexity.