Part of the issue is that you are making an unfair comparison...you are starting with the colony capital ship (progenitor) when you play advent but not with the colony cap when you play as TEC (akkan)...so, it may not be that you are playing terrible as the TEC, but rather that you made more economically oriented choices as the Advent...
Regardless of which faction you are playing, colony caps will always boost your economy because they allow faster expansion and less resources spent on colony frigates...I don't know the particular map you are playing but I do know some custom maps can be a real pain to colonize on if you don't have a colony capital ship...it's not uncommon for them to separate your HW from colonizable planets with asteroid belts, gas giants, and other uncolonizables...this makes using colony ships very difficult...
Your first change should be to use the akkan instead of the kol or marza...in general, you should almost always start with either a colony capital ship or carrier capital ship...in a few rare cases, starting with a marza or vulkoras can be useful in rushing an enemies HW...this is simply how the current version of the game is set up: carrier caps are extremely dominant while combat, support, and siege are marginal and generally require unique situations to justify their existence (Kortul and Marza probably being your two best non carrier/colony caps)...
Getting LRMs is also of paramount importance...in general, bombers and LRFs (long range frigates, so kanraks, LRMS, and illuminators) are the best units in the game...they have many strengths and very few weaknesses...as TEC, you arguably have the best LRF...
As Advent, building lots of disciples is a good idea, but only because Advent has a hard time getting illuminators early on...Advent is the only faction where rushing heavy cruisers is likely to be a good idea...if you are TEC, early fleets should be composed of LRMs, some garda flaks, and some hoskikos...eventually you will want to incorporate large amounts of carriers with bombers...only later in the game should you push for Kodiaks (TEC heavy cruisers)...
As TEC, rushing trade is very important...when you should build trade is heavily dependent on what game speed you are playing on and whether you play with quickstart on or off...in general, a TEC player should have trade earlier than an advent player (as TEC needs 2 labs where advent needs 3)...