It's pretty obvious that the loss of Mortiis, who composed the bulk of the symphonic parts on their earlier music including In the Nightside Eclipse was a blow to the strength of their compositions.
First of all, just to clarify, this is a debate between a 10 album (Anthems) and a 9.5 album (Nightside), so I don't have a ton to criticize about Nightside. That said, synths on Anthems are way more sophisticated and dynamic. On Nightside the synths mostly are restricted to romantic leads (albeit, most of which are awesome). On Anthems, there are still plenty of romantic leads, but the synths are also able to add different elements throughout the album, from more atonal textures (i.e. the end of Ye Entrancemperium) to subtle background tones (i.e. the pizzicato at the beginning of Loss and Curse of Reverence). Ultimately this gives the album far more range, depth and texture than its predecessore.
There are also many examples of attempts to shoehorn disparate musical ideas together and a general lack of a clear and consistent musical direction on the album. As a result, it lacks the focus of their earlier music.
This is critique is vague and therefore empty, at least for the moment. Please elaborate on what you mean by this and substantiate this claim with some examples.
I also think Ihsahn's vocals are pretty bad on the album, despite being more varied than ever. This would not matter as much if it wasn't for the fact that they are fairly prominent on the compositions.
The vocals are excellent and help accentuate the different thematic dimensions of the album. Since there's often a play of different personas, the interplay of clean and harsh vocals is especially effective. For example, this can easily be seen on the first two tracks of the album, where the protagonist is confronted with Evil. Of course, that's lost on someone who cannot or does not synthesize the conceptual and sonic dimensions of the work.
It's fairly clear that it's a transitional album that draws from too many sources while being hampered by personnel changes since their previous work. It tries to do too many new things at once, most of which are only explored at a superficial level.
"Transitional album" is a ridiculous critique. IX Equalibrium is a transitional album. Anthems is a total and complete expression of an artistic vision.
Also, calling it superficial is an empty critique. You seem to think identifying your position is a sufficient critique. EXPLAIN your position and support it with examples/evidence.