The 3D Scene in Dimension is poor quality compared to the render

he is talking about web preview i.e, the image a client in some other place sees when they look at the rendor online... in fact a lot of devices can't even see the image at all because they lack the Cpu or just block the network script

imo you are much better off to rendor a few [front + top] images locally and share those for your client instead of trying to use a gimmic web browser that Adobe doesn't really understand or support... image sharing softwares are every where with most camera software including the best free options

two high rez Jpg images will give your client better ideas of what the bottle will finish up as

In the upper right of the Dimension window there is now a Preview settings menu. You can have a quick approximation of what the final render would look like. Try the different options, and you may find one that is good enough for getting approval.

define "live 3D scene"

a web site needs the Cpu of the users device to rendor its image... given that could be anything from a Apple Mac to a Android phone the answer to your question is no

Q2 = a better program for interactive 3D product renders?

any machinima software example; Iclone, Unity and Unreal engine will blow away basic browsers for web viewing because they do the rendors at your end before uploading and the client device doesn't really matter as long as they have enough to download and run the basic file i.e, at least a digital phone less then 5 years old

Iclone is the best around $$$ but most hobby users start with Unity (Mac) or Unreal (Windows) because they are free... Adobe has nothing and is at least 10-15 years behind