~The questioner uses a Wookieepedia quote to illustrate their question, and I am adding this information as an answer only to point out that one illustrative quote is incorrect, even though they did say that Wookieepedia isn't always reliable. At the end, I add the little bit I can think of offhand about how Sidious thinks of Vader.~
Do not rely on one portion of the Wookieepedia "Palpatine" article that you referenced. It is in a paragraph that references the novel, Dark Lord:
The Rise of Darth Vader, and there is nothing in the novel about Sidious' relationship with or attitude toward Maul in the book. The paragraph seems to be mostly an opinion piece. Tomorrow, I will edit the following Wookieepedia Legends entry by removing Maul's name:
Though he had nearly left Vader to die back on Mustafar, Sidious held,
perhaps, the merest sliver of affection for him that he had never held
for Maul or Tyranus...
I will delete Maul's name because we know that, at least in Legends, which this Wookieepedia article is categorized as, that Darth Sidious did place some type value on Maul.
In Legends novel, Darth Plagueis, Plagueis thinks to himself that Sidious has an "almost filial" relationship with Maul.
In the novel, Darth Plagueis, Sidious becomes physically sick when he learns that Maul was killed by Kenobi on Naboo, which we all know now not to have happened.
Darth Sidious became physically sick in another novel, Lockdown, when his master tells him to let Maul die in Cog Hive Seven.
In the novel, The Wrath of Darth Maul, Sidious tells Maul that he values him the most.
Of course the term "value" can be taken literally, and we can say that Sidious placed a monetary value on his apprentice, therefore his apprentice was nothing more than property. This could easily be true and the very closest that Sidious comes to caring about something, but we have what Plagueis thinks about their relationship to help put some type perspective on it. What constitutes "filial" for a Sith is anyone's question, but I think that is the closest we're going to get to a Dark Lord such as Darth Sidious caring about or liking anyone.
Sidious is human, and at least in real life, a human can possibly become physically ill when something happens to someone they care about. A person, however, can also become physically sick when they lose valuable property.
The above are Legends references that I can think of immediately without digging through notes, books, etc, but we have a canon source that may help a little bit:
In the Marvel comic, Darth Vader #20, Sidious tells Vader:
I learned from the mistakes of my forebears. I used those who were
not Sith to achieve my aims. Darth Maul was a loss, but Darth Tyranus... He was a proton torpedo. He served his purpose and was gone...
It seems that Sidious "used" Tyranus to achieve his aims, and possibly we could even infer that Sidious didn't consider Tyranus a Sith if we interpret Sidious' words to be reflective of his exact intent, which I think we can. I'm sure there is argument here, but this reply isn't the place for it. I think this portion provides a nice comparison of how Sidious compared these two apprentices of his. He says he used Tyranus, yet at the same time he says that Maul was a loss, which to me reads that Maul was more to him than an asset to be placed into service. Perhaps this is evidence that Sidious did care about Maul and possibly clarifies the Legends content.
I have no idea how to compare this to Vader. Of what I've read, the child Anakin was of immediate interest to Sidious, and he did treat Anakin in close to a paternal manner. We know that he was manipulating Anakin, though. We have Legends and Canon content that gives us both extremes or at least an appearance of polar emotions toward Vader. In some of what is available, Sidious hated Vader for getting burned and actively sought replacements, which never really worked out for him. We also know that Sidious highly valued Vader. Sometimes they seem to genuinely refer to each other as "friend" and "old friend," but there are plenty instances when the term is sardonic in nature.
One perhaps-canon source that may be of benefit here is something that Dave Filoni and Sam Witwer said in a Hollywood dot com interview about reviving the character of Maul for the television series, The Clone Wars. They confirmed that what they were saying was reflective of what George Lucas wanted, hence why I said "perhaps-canon." No date is given for the interview, but it was published right before The Clone Wars season 5, episode 16, "The Lawless," what aired, which was February 2, 2013, in the US:
So, it’s the perfectionist streak that Palpatine has. And what’s
really fun to note is that Darth Maul, having survived his grievous
injuries, plants the seed in Palpatine’s head that maybe you don’t
give up on these guys so quickly. If they’re dead, or you think
they’ve been killed, maybe they’re not. Maybe they can survive, maybe
they can amount to something. That’s something we get to see coming
up, Sidious realizing that. That ultimately leads to Darth Vader.
...
Common wisdom would be, you find this guy lying by a volcano, his
flesh smoking and burned up, with no limbs, and you’d say, “Hey
stormtrooper, put a blaster bolt in this guy. Put him out of his
misery.” You don’t rebuild that guy. That’s ridiculous. Unless maybe
you’ve already seen a guy getting cut in half and crawling through
garbage for ten years, clinging to life with every ounce of
determination he has. That’s the nature of the Sith, they don’t see
anything beyond their corporeal existence.
It seems that Lucas brought back Maul so Sidious could see that there was a reason to spend time on an apparently broken apprentice; so he wouldn't leave Vader to die. Perhaps this could be understood as Sidious caring about the person more so than caring about immediately finding a replacement. The person is worth the time, but again, is this caring about the person or the investment? Perhaps there is no separating the two. Sidious did exploit Vader and his other apprentices, but that is what Sith do and it is what was done to him by his master. I'll close with this quote from the same interview, and perhaps this can help you make up your mind. I think that this is going to be more personal opinion in the long run because, as said earlier, there are many examples of both extremes that have been represented in the seemingly countless number of publications with Vader and Sidious in them:
The Sith training is nothing short of torture, so there’s always a
great deal of hatred built-in to the master-apprentice relationship,
an intense animosity. We see that between Vader and the Emperor in the
original trilogy.
I ended up spending a lot of time on this and am tired now and will leave it as it is. This is my first SE answer, so I ask for any helpful criticism. I hope we can edit these so I can update content later.
