There is no simple answer to your question. By the way, it's the 800mm f/8 ED non-IF lens head.
The lenses to compare are 300/4.5 ED vs ED-IF, 400/5.6 ED(PC) vs ED-IF, 600/5.6 ED vs ED-IF, 800/8 ED vs ED-IF, and finally 1200/11 ED vs ED-IF. All pairs except 400 has a non-ED version as well, which in general tend to give good image quality but increasingly troubles with chromatic aberrations of the axial kind as focal length increases. In cases known to me, the ED-variants have better image quality than any of the non-ED designs.
As I have most but not all of these lenses, I can only contribute some data points for paired comparisons. Other members are welcome to chip in with their observations of course.
300/4.5 ED vs ED-IF: ED has the best image quality and is near apochromatic, to the extent that there is no IR focusing mark. Focusing is slow and stiff compared to the ED-IF version, which is super snappy and can be focused by a single finger tip. The ED-IF also handles added extension well and one can enjoy close-ups around 1:3 to 1:4 scale. For shooting into bright light sources the ED-IF performs better.
The ED 300 is elusive and difficult to track down in particular if you wish to have a clean specimen without too much external signs of wear. The ED-If is easy to get, either as AI or the more common AIS. The latter has the best tripod mount. Be aware that many times the ED-IF version simply is labelled '300/4.5 ED' by ignorant (?) sellers, thus make sure you read the description and study any pictures if tempted to buy. The ED-IF has a characteristic shape with a front section followed by pronounced narrowing into a slimmer focusing barrel, the ED lacks this appearance and well -- looks like a lens
The ED also has a quite tiny tripod mount platform. For tripod use, the ED-IF is is the true 'upper crust' in terms of stability if you have the AIS version. The AI has a narrower tripod mount yet still superior to most other lenses.
400/5.6 ED/PC vs ED-IF: Again, the ED has the better image quality, but the ED-IF is not far behind. The latter also focuses much faster, but is less easy to deploy safely on a tripod as it tends to wobble a bit due to its long and light weight build.
The first generation of this 400 is not labelled 'Nikkor*ED', only -PC (or in the onset, simply -P). Only *ED units have the gold ring. They are externally and internally similar but might be not identical in optical terms. However, from the samples I have used over the years, performance is well-nigh identical so I lump all non-IF versions together. My current version is a modified K lens of the 'PC' type.
800/8 ED vs ED-IF: In terms of image quality, the ED wins hands down. However, the ED-IF handles far better as it is much more light weight and less bulky because no need for the cumbersome focusing adapter. The ED-IF also focuses much closer, to 10m instead of 14-15m of the non-IF version.
Whilst the 800/8 ED-IF is uncommon and scarce, the 800/8 ED lens head is amongst the rarest of Nikkors and less than 100 units were produced. I would look for the bigger 800/5.6 ED-IF Nikkor instead.