you can clear militias faster with a Battleship but you cannot colonize planets faster because you are limited by two things.

the first limit is the antimatter supply on the Colony frigate. its stuck at 225, much lower than what cap ships have. it also has a much lower antimatter recharge rate and it loses a much greater amount of antimatter when it phase jumps. colonizer cap ships rarely do not have enough anti-matter to colonize a planet, colony frigates on the other hand run out very quickly. you'll be waiting on AM recharge alot once you're more than 1 jump away from homeworld.

the second limit is the inability of a colony frigate to go in and make a "hot drop colony", which is a phrase i use to indicate colonizing a world before the militia is cleared. the colony frigate is fragile and is a militia magnet. its not safe to bring it in until all the light frigates, heavy cruisers, and lrms in the grav well have been destroyed. with a colony cap ship on the other hand all you have to do is kill the siege frigates (which die very quickly to light frigates) and you can colonize the world while still fighting. in fact, you can then go and build some turrets and repair structures to help you finish off the militia. its possible in this way to colonize very heavily defended Terran or Desert worlds much earlier in the game you would normally be able to if you were only using colony frigates.

a final factor, while not a strict limit, is the bonuses you gain from using a colony cap ship. an Advent Mothership reduces the planet infrastructure costs of new colonies for a few minutes. a Vasari Evacuator makes structures build 20% faster for a few minutes. the TEC Akkan can add some free extractors on the resource rocks. these are side benefits that you can't get from the colony frigates. 

I see, thank you all for the info. For now I try small maps of 9 planets with 1-2 choke points.

Tomorrow I will try to expand with the Vasari "egg" Capital ship followed by assailants once I want to see how this will work out.

Must be fun to colonise a planet faster than the destruction of the orbital structures. As assailants seem quite tough I might as well try some early harassement on undefended planets and continuously resupply my main fleet with new assailants till I have enough for better defended targets.

Thank you all again.

I don't like the idea of "No light frigates".  If you just depend on your colonizer cap ship to clear out that volcanic/ice world, your opponents will have colonized half the map before you are able to move on.  They are a must if you get stuck with nearby terran and desert worlds.

its just not true though. light frigates do just fine, especially for early colonizing. they kill the Siege, Flak, and Kodiaks that are so common in planet militias more efficiently thatn LRFs do. i'm not saying you should go and build 10-20 light frigates at the beginning of the game, thats clearly a stupid idea.

i'm saying that 4 or 5 lights makes a great escort for a colonizer cap ship and will greatly assist your colonizing speed for several reasons. just killing things faster is helpful in its own right but thats not the only benefit you gain out of it. it prevents your cap ship from having to sustain too much damage from planet militias, which means if you encounter significant enemy resistance (if he's rushing you, for example) you're not too likely to have to retreat your cap. 

they also work wonders for controlling neutral extractors. shooting up the scouts and colony frigs that people send to neutrals makes a big difference and light frigates are very good at this. they're also way fast and can actually get out to those neutral extractors faster than anything except scouts. 

don't dismiss them just because they get killed by LRFs. 

Since mid-late games have players spamming all kinds of support cruisers, I wouldn't call LF obsolete after a couple minutes. 

the reason Assailants do so much more damage than Skirmishers is because of their damage type.

Assailants do anti-medium type damage, which has good performance against almost everything. it does alot of extra damage to Light frigates and either 75% or 100% damage to almost everything else. 

Skirmishers do anti-heavy type damage, which is somewhat less potent. it does pretty good damage to heavy armor (the armor type of most cruisers, and also the Flak frigate) but doesn't do very good damage to anything else, its getting reduced to 75% or even 50% damage against alot of things. 

on top of the damage type difference Assailants have longer range and higher base DPS in general. they're much more effective on offense. thats their role really, offensive specialist. 

finally, it is incorrect that Assailants lack upgrades. in fact they have the most weapon upgrades available of any Vasari ship. you can research 8 upgrades for Phase Missiles and these upgrades effect both Assailants and your strike craft squadrons. the first 6 of those upgrades grant Shield Bypass, which is an amazingly potent effect. it allows missiles to have a percent change to completely ignore the shield and strike the hull directly. in addition to the direct hull strike a bypassing missile disregards shield damage mitigation so it will always deal 100% of its damage, if it bypasses. its friggin awesome. the last 2 upgrades on the missile path just provides +20% damage, boring but effective. 

I use almost that exact tactic all the time, minus the colony frigate and scout. I start out by building a scout, then sending it on it's way, and then building a colony frigate, which I leave at my base so it doesn't die. Next I build a Battleship, then pair it up with 5 light frigates and go on conquering. I conquer 2 or 3 plantes, find a choke point, and set them there until I get another fleet. If I have enough money, I will make small task forces of light frigates for planetary defense and to eliminate defenders at neutrals. I find it very effective.