White Star is the new and popular kid on the block. I agree that it's really nice if you want a space opera game with old school D&D rules and 100% compatibility to Swords & Wizardry WhiteBox. I'll write more about it soon.
That being said, my favorite D&D ruleset is Whitehack at the moment.
But can't we have the best of both worlds?
Whitehack (WH) is also based on S&W so conversion is totally possible. It would be easier to take Whitehack's 1st version as it was closer to S&W, but I appreciate the 2nd version for its unified task mechanism. Plus, you can't get the 1st edition anymore.
The idea is to take Whitehack's mechanisms and the fluff of White Star (WS). WH's character generation is pretty versatile so everything should work without much need for modification. Even alien races are easy to model as races are just groups. WH separates race and class.
Let's try to build some level 1 characters for White Star's default setting in the Kelron sector. I'm going to roll 3d6 in order, so the characters are not optimized.
4 sample characters
Brendon Konicek, Human Deft Aristocrat
Str 9, Dex 17, Con 11, Int 12, Wis 12, Cha 10 (Resistance)
HP 5, ST 7, AC 2, MV 25, AV 10
Attuned: Fine Clothing, (Communicator)
Laser Pistol (1d6+2), Kevlar West, Belt Pouch, 2 credits
I chose Deft for the Aristocrat because the Wise class gives him miracles (a.ka. spells) which wouldn't be what I'm looking for here (that would be more appropriate for a Star Knight or Alien Mystic). Brendon has 1 slot for attunements (a Deft character specialty). He is attuned to Fine Clothing, so if he's wearing them and wants to impress others he'll get a positive double roll (think Advantage in D&D 5e terms). Likewise, his "inactive" for the slot is a communicator so he can use his silver tongue with this device, too.
His vocation group is being an Aristocrat, his second group is being a member of the Resistance (tied to CHA). His affiliation group ensures that he has Resistance contacts but also needs to be wary because he's an enemy of the Galactic Consortium.
Whitehack's movement rates differ from White Star, but you could take WS' rates if you prefer. That would also ensure compatibility with spaceship combat.
D'Kura, Qinlon Strong Mercenary
Str 11 (Quinlon), Dex 14 (Mercenary), Con 12, Int 14, Wis 12, Cha 6 (Quinlon, Resistance)
HP 6, ST 5, AC 5, MV 25, AV 11
Melee option 2: push
Heavy Armor, Battle Axe (1d6+1), Breathing Mask, Flares, Flashlight, 10 credits
Here is a melee combat machine. Not sure if WH's melee options port over to sci-fi as seamlessly but for now I don't change them. D'Kura has Quinlon as a species group, so that's positive for strength related feats but may be invoked negatively for Charisma. She's also a member of the Resistance.
Her vocation group is Mercenary. I tied it to DEX and it will give her bonuses for dexterity-related tasks.
Loran, Oday Wise Mystic
Str 15 (Oday), Dex 9, Con 6, Int 9, Wis 13 (Oday), Cha 7 (Resistance)
HP 7, ST 6, AC 2, MV 20, AV 10
Leather Vest, Staff (1d6), Med Kit, Recording Stick, Communicator, 4 credits
"Stupor", ("Hold Portal"), ("Purify Food & Drink")
Loran can choose two miracles per slot, but only one is active. He has another inactive slot for miracles as he has a Wisdom score of 13+. I just copied the level 1 Alien Mystic Gifts from White Star for the sake of simplicity. WH's miracles system is pretty open-ended and versatile so you can also go another way and choose more free-form miracles if you like. For a Star Knight/Jedi, you could write down something like "These are not the droids you're looking for" and it would be fine as people know how that's supposed to work.
Y3-JG, Robot Wise Pilot
Str 9, Dex 13 (Pilot), Con 14 (Robot), Int 9, Wis 8, Cha 7 (Robot, Resistance) HP 3, ST 6, AC 3, MV 25, AV 10
Light Plating, Laser Pistol (1d6+2), Toolkit
"Binary", ("Mechanical Wonders")
This one is a bit curious because it's a mix of three concepts: WS' Robot and Pilot class with WH's ability to work miracles. Because I didn't want the PC to be able to have Meditations or Gifts like the Alien Mystic or the Star Knight I opted for "scientific"/mechanical miracles.
As I'm going for WS' fluff with WH's mechanics there is no need to write down the Robot class abilities like Metal Body or Self-Repair. Likewise, I don't need to take the Pilot Class abilities slike Jury-Rig into consideration. Everything is covered by the species and the vocation group.
This concept really shows how versatile WH's character creation is but also shows that a lot of it is based on the narrative instead of "hard" mechanics.
I didn't roll up a Star Knight this time. WH also comes with a corruption mechanic so you could use that to model light side/dark sight powers.
So, does this whole thing work?
In principle, yes. However, you forgo White Star's sci-fi specific class adjustments. This is most obvious with the Pilot class. Stuff like Stick Jockey or Reroute Power give rules for starship combat which are missing from Whitehack.
However, you can do a lot with WH's groups so if your character is a Pilot she will automatically get bonuses for related tasks (see WH's section about Skills & "Trained Rolls" on p. 15).
Let's take Jury-Rig for an example (WS p.20):
JURY-RIG: Once per day a Pilot may attempt a quick fix on a starship. This takes one (1) round and restores a number of Hit Points to the starship equal to 1d6 per level of the Pilot. [...]
With WH, you would rule that the PC has to make a "trained Dex roll". If the PC isn't a Pilot she would need to make a negative double roll (Disadvantage in D&D 5e terms). If the PC has Pilot as a group somewhere on the character sheet she can make a normal check. And a PC with Pilot as a group for DEX would even get a positive double roll.
As a result, choosing Pilot as vocation will ensure that you are good at flying ships, space combat and tinkering with your spacecraft and gives the same flavor as WS' Pilot Class.
Does it make sense?
It depends on your personal preference. I'm happy with White Star when I want to play old school space-opera sci-fi. It works out of the box and has familiar rules. Whitehack is more "Neo-OSR" and incorporates some modern/indie/narrative concepts which I really enjoy. It is flexible and also suited for other genres. One could take WS' starship rules and port them over to WH. Still, that's work which needs to be done.
I have a few friends who are not so much fans of old school D&D but could perhaps be convinced to play Whitehack as it mitigates some of their concerns (class restrictions, race-as-class, XP bonus for certain stats etc.). For this reason, I would use Whitehack.
Other than that, I am probably too lazy to convert the material as I also see no fault in using Swords & Wizardry WhiteBox/White Star and see no need to overcomplicate things.