They work pretty well together, in my experience
Granted, this is experiential because trying to crunch their entire pile of capabilities is just not a thing.
But my short answer is "Yes. You can run a Mixed Solar/Lunar game and it will be reasonably balanced." My "evidence" is that I've run two games with mixed Circles, and it went well.
The longer answer
The power difference between Solars and Lunars is 3E is narrower than it was in 2E. Solars tend to operate more like "First among peers" than "A class of their own." But the big thing to remember is that Solars and Lunars are powerful in very different ways and trying to use one like the other is not going to go so well.
Solars favor specialization (see: Supernal Ability). They have very deep Charm Trees tied to specific Abilities and trying to branch out from their specialization gets very expensive from an XP Perspective. A Solar Archer wanting to get good at Knife Fighting has to start a Charm Tree over from scratch.
Lunars favor flexibility...their Attribute-tied Charms tend to be more broadly applicable, but less specifically overwhelming. A Lunar Archer who wants to pick up a knife probably already has a battery of Dexterity Charms that will work on both. And it's vastly cheaper to buy up extra skills than it is to buy up a whole new Charm Tree.
The practical output of this is that if a Lunar goes head to head with a Solar in one of that Solar's specialties, the Solar will generally have the advantage. Especially if it's their Supernal. After all, if you're all Essence 2 but the Dawn is flinging around Essence 5 Brawl charms...that's gonna hurt.
But for a Lunar...just to give an example, Striking Mospid Method lets you reroll dice on a withering attack. Any withering attack made with Dexterity. Shoot a bow? Striking Mospid Method. Throw a knife? Same thing. Stab em? One Charm works on anything.
In the same way, Solar Excellencies are easier to come by and you don't have to Stunt to get the most out of them...but a Lunar Excellency applies to a broader set of things. You can throw Excellencies at tests that you don't have a single dot in that ability, and you can always try to stunt to use your best Attribute to boost your dice cap.
All of this together ends up meaning that, at least in my experience, Solars and Lunars actually work really well together. They are similar enough in raw power to be comparable and the ways they are different can create really neat dynamics in the group.
In fact, in one group I led, it actually resulted in the Solars specializing more because they felt like the Lunar's broader abilities did a far better job covering any of the gaps that they felt like they needed to 'dabble in' so as to not have gaps in the party's capabilities.
And, at least for that group, everyone liked it. I'd briefed them on this same sort of talk before we went into the game, so they knew what to expect. The Lunar players enjoyed the fact that they had this wide range of things that they were solidly good at, and the Solar players really got into trying to figure out how to take the--like--three things their character was absolutely insanely good at, and apply them to as many situations as possible.
The Big Difference
The sheer absurd nonsense that Solars can get up to with Craft and Sorcery is unrivaled. But most of the really high-end nonsense is beneficial to the entire party and tends to function more as a Force Multiplier than anything else.
After all, if the Twilight Craftsman just made this bonkers Artifact 5 Grand Daiklave...well, makes a lot more sense to hand it to the Melee Combatant than to swing it around themselves.