In my answer, a tab, short for tablature, is a form of music notation for an entire song that plots the individual notes marked as fret numbers on each string. A chord diagram is the graphic that shows where to place the fingers on the fretboard in order to play a specific chord. Different forms of music notation, including sheet music, lead sheets, and tabs, are often accompanied by corresponding chord diagrams.
To show chord diagrams in text form, I will use the common practice of writing a string of 4 characters to represent each string from G to A with a number meaning a particular fret, a 0 meaning the open string, and an x meaning a muted string. As such, the common C major chord all ukulele players learn will be represented by 0003.
This is not consistent with the wording in the question; the question is currently written so as to mean that each chord diagram is a "tab" and thus a song has "tabs" to show one how to play the chords. To avoid confusion, I will write this answer in the more technically precise way - a tab is not the same as a chord diagram.
First of all, I can tell you why Sibelius came up with that chord symbol. I haven't used Sibelius in a long time, but my guess is that you had the notes [E G# B] written on the treble staff and then asked Sibelius to produce a chord diagram for that chord in the staff notation. My other guess is that you could also have asked Sibelius for a chord diagram for an E major chord. In either case, I think Sibelius interpreted this very literally. I suspect that Sibelius thought something along the lines of:
An E chord has the notes E, G#, and B in it. Let's map those notes onto an ukulele fretboard to create a chord diagram.
The lowest fret position that makes an E note is the open E
The lowest fret position that makes a G# note is the 1st fret
on the G string.
The lowest fret position that makes a B note is the
2nd fret of the A string.
All the notes of the chord are accounted for. Let's mute all remaining strings.
Therefore, an E chord is fingered as 1x02.
I would guess that Sibelius has an algorithm to find chord diagrams for any notes or any chords on any string instrument tuned any possible way. However, there are always many alternative ways to play a chord, and what Sibelius finds to be the best diagram won't always align with what a human would decide upon.
All chords have alternate voicings and fingerings. When assigning chord diagrams to any form of music notation, one is recommending to the performer a particular way of playing the chord, and unfortunately the E major chord is one of the least agreed-upon of the common ukulele chords. Context will matter a lot in determining what particular diagram you decide to endorse. I would recommend generally staying consistent, so one diagram should work for all the E chords. Let the player decide if there's a reason to switch it up.
The website linked in the question lists 4442 for the E major chord. This is a very common fingering for this chord. Some players "collapse the knuckle" to barre partially at the fourth fret, others use all four fingers on individual notes. I use and recommend this voicing because it is a moveable shape that can be easily applied in other places on the neck, as well as the fact that similar related chords are easily accessible from this position such as 4444 (E6), 4445 (E7), 4432 (Em), 5553 (F), and 4222 (Bm) for example.
On the other hand, this is one of the most complained-about chords I know of for the ukulele and can be difficult for beginners. Collapsing the knuckle to avoid touching the A string can be a real obstacle to the unexperienced, and cramming three fingers into the fourth fret area makes for a very tricky alternative to that barre.
The other main contender for the title of definitive E chord is 1402. This voicing has some serious advantages: with this shape, barring is unnecessary, and every fretted note is spaced far enough away to allow for cleaner fingering. It even has an open string in it, only requiring three fingers to play. I used this as my E chord for a long time when I first began playing, and I still recommend it to others who have trouble with 4442. I've even read some ukulele books that prescribe this 1402 shape, although a majority still list 4442. It does have its own set of problems, though.
This chord shape is not moveable, since it has an open string. Where 4442 can be slid up and down the neck to make more major triads, 1402 is much less versatile and only works in that position. Not only that, it doesn't lead as well into related chords around it. 1202 (E7) requires a repositioning of the entire hand, as do 2100 (A) and 4432 (B). While it is close to 2402 (Esus), it lacks an intuitive path to get to 4422 (Esus2) or 4402 (E5). Most of the chord transitions to and from this chord will end up being extra memorization; muscle memory for these movements won't apply as easily to other common chord changes since the 1402 shape is so specific. And for experienced players, it is much harder to add an extra finger somewhere or slide one around to add some flair with this 1402 shape than with 4442, which practically begs to be played around with.
Sibelius, though, came up with the ostensibly simpler 1x02 fingering. Although most ukulele chords are played with all four strings sounding regardless of how many unique notes appear in the chord, it is possible to learn to mute some strings while letting others ring out. This can be used to find easier alternatives to some tough shapes, and sometimes a mute can be avoided altogether with an extra-precise strum that avoids the string to be muted entirely. Many players do learn either muted-note chords or string-skipping strumming techniques, so for them this 1x02 chord may be a good alternative.
Personally, I have never adopted muting notes in chords or targeted strumming into my own playing, since my playing style diverged from the situations where those kinds of chords would be potentially viable (I do a lot of fingerstyle/fingerpicking). It is definitely possible to get away with neglecting these types of chords if one is willing and able to learn enough four-note voicings to cover all of one's bases. Moreover, these chord voicings will lack familiarity to most readers since all common chords have at least one standard way to play them that does not require muting.
In any case, I would argue that 1402 is just as easy if not more so, and one would have to use three fingers anyway - why not play that E on the fourth fret instead of having to lightly touch one string while pressing hard on the others? Additionally, this 1x02 is a bit of a "crutch chord". Like 1402, this is not a moveable shape so it lacks the versatility of 4442, and it doesn't lead into and from other related chords as well as 4442 does. I would not recommend 1x02 unless muting strings is already in the player's arsenal, and so for the most part I would not give the 1x02 chord diagram unless other muted-note chords will also appear in the music. For ease of performance, either categorically avoid all muting shapes, or prescribe them wherever it makes a chord easier.
There are lots of other options, especially if one looks higher on the fretboard. Here is one example source that lists some alternative ways of playing an E chord.
How does one decide what chord voicing to display for a song? In the general case, go with the most universal shape for the chord. Most chord diagrams written for songs are placed for the benefit of a less-experienced ukulele player who may need a quick reminder on what the desired chord looks like (or may even not yet know how to play a certain unfamiliar chord).
Chord symbols typically are located in one of two places: right next to every place where they occur in the music, or each chord in the song listed once at the top of the page. If they are at each specific location, it may be possible to suggest specific chord voicings for each instance, but beware that beginners will often either be confused by this or ignore it completely, and advanced players will already be aware of your suggestion and won't need the reminder. In a teaching context, it can make a lot of sense to show multiple diagrams for the same chord at different times (one potential example is the "pinky G" variation on the G chord that moves more smoothly to E7 but does require the pinky finger to be involved), but generally this is counter to the style of chord-diagrammed notation.
Chord diagrams are intended to demonstrate one definitive way to play the chords in question and are not intended to be absolute prescriptions for the only correct way to play the song. Experimentation and deviation from the exact chords given is to be expected and welcomed, and the more experienced players will come to their own conclusions about what exact chord voicing is best in each case. If explicit information on how to play each chord is deemed necessary, tablature or even fully-realized sheet music (gasp, shudder) would be a much more appropriate notation option!