If you can't win by brute force, you do have many other options. One very simple approach is to attack somewhere else. The enemy fleet can't be everywhere at once, and certainly can't spam defenses everywhere. Try probing him at another location and if it works start pumping units there. Maybe open multiple fronts to keep him on his toes.
When attacking, you don't need to fight in the range of repair platforms or starbases. You can move off to the far side of the planet and sit there. You can simple bomb the planet from there or pepper them with strike craft. You don't need to engage them where they're at their strongest. You could also sit back and build a starbase to lock down the enemy gravity well and then drive them out once it completes.
Siege frigates are risky to use. If you're attacking undefended planets, they're good enough, but if there are any defenders nearby these units are simply out of the question; too easy to kill. However, you can use capital ships to the same effect. The Vulkoras Desolator is a great pick for this purpose. If specced appropriately, it does nearly as much damage as an equivalent cost of siege frigates (at level 1!) and is many orders more difficult to kill. If you want to bombard in battle, the Vulkoras is your unit of choice.
You could also play the long-term and build up your economy while keeping their's in check. This is very difficult to do and usually requires playing smart with a smaller fleet. If you can maintain a 50% larger economy for ten minutes, you should have no problem crushing your opponents.
As for units to bring in, the good ones are carriers, flaks, and support cruisers. The Overseer is great for keeping capital ships and starbases alive, while the Subverter is one of the most devious tools you can employ. Vasari are privileged in that their assailant, sentinel, fighters, and bombers all share the same damage upgrade (the awesome phase missile), and these four units together make one of the most balanced fleets possible. There's virtually no reason to go with a heavy-cruiser based fleet as a result.
For capital ships, the Skirantra is your best bet, but long-term you may want to consider the Vulkoras and the Kortul. Jarrasul and Antorak aren't bad, just overshadowed by the other options.