The Shadow "knows"

[Crystalion]

Can I conclude from this that for casting, putting on a plus three shadow great helm of restoration, rather than a plus two assassin skill rare diadem is probably a mistake?

In the first case the shadow master level is 28 and in the second it is 29.

AFAIK best would instead be any +3 shadow tree Diadem, whether rare or magical, worn just for the summon.

While 29 is better than 28 for the SM slvl, for various stats (DR, HPs, AR, resists, etc.), it won't help with the shadow_slvl/3 factor, as both are the same as 27. That is, all have a "bonus" value of 9 when the SM later casts skills.

Don't forget that skill shrines (+2) and Battle Command (+1) can bump your SM slvl "permanently" when used at the time of summoning.

Whether giving up slvl 29 stats for slvl 28 stats is worth the possible random affix goodies is unknown.

As the ilvl of the rolled great helm is pretty high, with that high a level shadow... 24+29*3 = ilvl over 99! Whether this is capped at 99 in v1.10 is open to question (Ruvanal and I determined that items are indeed sometimes over ilvl 99). Even if it was capped at ilvl 99, the old v1.09 affix calculator suggests an alvl at that point that is effectively unlimited. So the difference would amount to the fact that the set of possible affixes allowed on circlet class helms is much bigger, and includes various +skill stuff that can't occur on the great helm.

Whether the Shadow would benefit from these affixes, if rolled, is subject to game mechanics (many probably don't have an effect) and also to your opinion as to their value. Some of the differences I see listed for v1.09 at least, include Magic Find, life stealing, life everlasting, +trap skills, fast cast rate, substantial resist all, etc. There could be quite a difference, potentially, in the effectiveness of the shadow, from these affixes. But this looks, to me, even harder to judge this at time of casting the shadow, than for a valk.

If you were planning on a long play session it might be worth it to summon a number of candidate shadows, and test them, carefully ;D , PvP. Life Everlasting, for example, can be readily discerned this way. Her resists can be probed (you might just be able to cast repeatedly until you find one that, by testing, proves immune to desired elemental damage, even without Fade...the diadem sure looks to me more likely to achieve that).

But generally speaking, you should do what is fun for you.

The case is a bit different for low slvl shadows... one should prefer the circlet..diadem strongly in those cases (because of the high net affix level, e.g. a slvl one shadow still has access to all affixes on/via diadem).