Never driven one, but being a t/c auto, I'd have no major concerns over reliability or smoothness.

I'd maybe worry that the EAT8 might hunt about, never settling on one gear (but that would probably be an irritation all of these modern auto boxes with too many gears), but the EAT6 should be OK in that respect.

Not 100% sure, but I think they are made by Aisin.

I'm sure John F will offer up some direct experience from his 2008 at some point.

Reliable?

Very. Aisin's AWF6F25 (and 45), otherwise known as EAT6 (Efficient Automatic Transmission 6 gears) in Peugeots, now superseded by the EAT8, was made in huge quantities between 2005 and 2019, and found all over the world in all sorts of vehicles. Unless worked hard in heavy cars/vans or towing stuff, it requires no fluid changes. In light unstressed cars like our Peugeot 2008 it will probably still be as good as new when the car eventually dies.

Smooth?

Yes. It's of similar design to the ubiquitous 'tiptronic' 6HP box of that other world famous gearbox manufacturer, ZF. It is highly 'intelligent', always finding the 'right' gear. I find the 'kick-down' almost instantaneous in response. It is set up in our 1.2 puretech 130hp to be quite high geared (30mph per 1000revs in 6th), only changing into top gear at around 57mph, so if trundling along a level or downhill road I sometimes snick it manually into 6th. It never allows the engine to labour - even in manual mode it will change down if it doesn't like being in a high gear, and it won't allow you to change up if going too slowly.