The Erebus would probably have the edge if it could get off multiple volleys from its forward beams at a distance, but the Solaris should still have the close-range edge with its turret-popping Gattlers and Apoc missile massacres.
The Solaris would be able to come out on top, I think, if it exploited the UEF's superior strikecraft and strikecraft-mounted weaponry. If the Erebus doesn't have the newfangled beam shutters, a wing of Uris from the Solaris should be able to easily knock out both of the Erebus's forward beam cannons with Archers and Paveways, from outside of the Tev fighter screen's instant-kill range, taking out a lot of the Tev destroyer's firepower in a few seconds of shooting. They'd get Trebbed or killed by interceptors, of course, but taking out the Erebus's strongest weapons should give the Solaris the edge it needs to win in a close-up brawl. If the Erebus does have beam shutters, it would make the UEF's task a lot harder, and maybe require heavier weapons, but UEF bombers or gunships should still be able to do it, especially because the Erebus would have to open its shutters to fire the beams. (I don't know exactly how beam shutters will work, so this is an educated guess.)
The Tevs, by contrast, would have a much harder time defanging the Solaris. The Solaris's firepower is more evenly-distributed among a lot of turrets and missile launchers, rather than being more centered around a few vulnerable beam cannons, so Ares pop-up Treb snipers would need a lot more long-range shots to cripple the Solaris's anti-capital battery than the UEF Uris and Durgas would need to take out the Erebus's beams.
The UEF has other important strikecraft advantages, too. Uris with Slammers would be able to slaughter Tev fighter and bomber formations, unless the Tevs used wider formations. Tev bombers, as we know, are unimpressive, especially when attacked by UEF interceptors. Their Maxims would give them a little extra hull damage, and might take out some turrets, but they wouldn't live long enough to get a lot of Maxim rounds off, if the UEF interceptor pilots are competent. Though I don't have a lot of experience with them, I think that a well-positioned attack group of UEF bombers would probably do more hull and subsystem damage to an Erebus than a similarly-sized Tev bomber raid would do to a Solaris. The Tevs do, admittedly, have Trebs; a mass pop-up Treb strike, timed to coincide with with a heavy fighter/bomber push, could really do some damage to UEF strikecraft. Still, the UEF's strikecraft edge should hold true, and that, if anything, should hand the UEF the victory.
From what I know, I'd think that the UEF's superior electronics should give them an ECM edge, though I don't know enough about BP electronic warfare to tell you exactly how that would affect the battle.
So, all in all, unless I'm really missing something, the Solaris looks like it has the better chance of winning.
