This review covers the Prologue, Season One and Season Two. My ratings are 6/10, 6/10 and 5/10 respectively. There are spoilers in this review.
The prologue/first few episodes of Unlimited Budget Works establishes the Fifth Holy Grail War; a battle royale between seven servants (made up of mythological figures such as Heracles) and mages where the last survivor is rewarded with being presented the Holy Grail which can grant them any wish they desire. During these episodes it is emphasized how dangerous this war is where even witnesses of the war will be murdered. Then in episode three the feeling of danger for our protagonists disappears in an instant when Ilya decides to suddenly quit her battle with Rin and Shirou for no reason and go home. This doesn't get followed up on nor does it develop into anything. Perhaps my expectations were too high expecting fights to have an impact from the beginning, but these kinds of moments happen frequently. Some examples include; Archer's many chances to kill Shirou, Caster and Kuzuki not finishing off Shirou and Rin in episode ten and every fight where Gilgamesh is involved.
With the characters not taking fights seriously, another way to create tension in these fights is to emphasize the stakes of the Holy Grail War. To an extent, this works in UBW. The mages and servants eventually get eliminated, there are stories of innocent people disappearing or dying and the end game for Gil involves attempting to kill everyone. But these aren't executed well. The mages and servants would have their backstories explained in the episode they are about to be defeated, making it predictable. The innocent people's deaths are left in the background and their effects are never seen.
As for the end game, only a simplistic understanding can be gained from it due to the lack of explanation of the history, function and importance of the Holy Grail. All that's told by the show is that the Holy Grail may potentially be able to grant a wish of some kind, it can be used for evil, might not even require the war to be summoned and can be summoned by using a mage as a host. The Holy Grail itself appears as a pink blob. Most of these things get explained properly in other Nasuverse publications, however I believe that for a better viewer's experience they should have tried to address these problems in UBW. Nevertheless, they already have sequels planned so perhaps they will go into more depth then.
The focus of UBW is the emergence of Shirou as a mage. As a protagonist, Shirou comes off as a generic anime male teen with a naive mindset. He is a self proclaimed "hero of justice" because apparently everyone needs saving and only he can do it... by murdering people. If this show had a darker tone he would sound like a crazier version of Batman. Sadly though, the only exploration of his naive ideas and any other themes in UBW comes during his battle with Archer, which mostly involves repeating lines ad nauseam. There is also a forced romance thrown in to attempt to show Shirou's progression. He's not terrible as a character, but he's nothing special either.
The other characters in UBW lack development. Some characters will be given short backstories before dying, but no characters show any real change. The closest are Saber and Shirou deciding that they're proud of themselves. Rin simply stays as a typical tsundere for the whole show. An argument could be made that there wasn't enough time given to character development. However, there would be more than enough time if the pacing was improved. For example, the character monologues during fights (Shirou vs Archer especially) could be edited down or episodes such as Winter Days, Faraway Home could be condensed into a few minutes. While I feel the phrase "show, don't tell" is overused, I believe it is appropriate in this case.
There are other issues and potential plotholes that could be nitpicked, such as Archer not having any knowledge of his earlier life, but I'd rather now look at the positives in UBW. The animation is incredibly fluid, especially during fight scenes. The incorporation of CGI feels natural and makes some scenes a real spectacle to watch. The sound effects are great and the voice acting is satisfactory. These technical aspects alone are enough to make UBW watchable. The soundtrack adds an extra level of enjoyment, especially the fan favourite OP Brave Shine by Aimer.
Even with all the faults in UBW, the journey the characters go through is enjoyable enough to make this show satisfactory. Watching this won't be a special experience and other than the fight scenes, most of it will be forgettable. Nevertheless, unless you're a big fan of the Nasuverse, I wouldn't recommend going out of your way to watch it.