I think it would be interesting to chart up what the 'role' of each race/faction is in terms of the metagame. By metagame I here mean things like how the TEC are geared towards defensive, economy-focused play and how they should therefore typically adopt a playstyle where they attempt to maximize these traits in their play. I'll start out providing my analysis of each race and faction but I'd appreciate to have some of the much more experienced players I know follow these boards correct and add to my findings. Alright, let's get to it.

TEC

Strategic doctrine: Defenses and economy. This is the 'turtle' faction: Hunker down and hold the line using your superior defensive orbitals and starbases while you wait for your superior economic structures and upgrades to give you enough of an economic advantage to simply overwhelm your opponent using not superior units but raw macro economic power. Their ships and structures reflect this and are durable and heavily armored.

Specializations: Hulls & armor, economic upgrades

TEC Loyalists

Strategic doctrine: The basic TEC doctrine taken to the extreme: Even more heavily geared towards defense using tactical structures. Loyalists will play passively and not lash out at opponent territory, instead waiting for the opponent to come to them to take advantage of their superior defenses. They will be building lots and lots of tactical structures and starbases - especially the latter - and field smaller mobile fleets than normal whose main purpose is simply to keep the empire alive long enough for the superior economy and super weapons to be put to use. 

Specializations: Tactical structures, starbases

TEC Rebels

Strategic doctrine: The antithesis to Loyalists, Rebels are much more geared towards aggression. They are still TEC, however, so the general defensive doctrine still applies. This means Rebels will play out in a more balanced way. The Rebel commander will still likely choose to stay on the defensive and fortify for the early game, the goal being to wait until the Rebels' second specialization can be unlocked: Neutral faction diplomacy & pirates. At this point the Rebel player will switch into an offensive role, coordinating his attacks with hired pirates to overwhelm defenders. The Rebel late game is about spending income on a combination of ships and pirate bribery rather than the Loyalists' continued defense.

Specializations: Planetary assault, neutral faction alliances

Advent

Strategic doctrine: The Advent sit in the middle between TEC and Vasari, between defense and offense. What this more concretely means is they have this method of advancing where they build up a world with strong defenses then use their superior culture to neutralize - or at least gain the upper hand in combats on - nearby enemy worlds, then reinforcing these new worlds and spreading culture further. They are therefore 'offensively defending', so to speak. Culture plays the all-encompassing central role for the Advent player and spreading culture is the prime priority.

The other central aspect of Advent play is shields & shield mitigation. The Advent faction boasts the most powerful shields with the highest mitigation rates. This lends a 'guerilla warfare' aspect to Advent combat, the idea being that they will attack, deal some real (hull) damage to opponent while own superior shields are still up, then retreat to recharge shields only to return to battle having taken no real damage themselves shortly thereafter. Advent combat style therefore has them constantly pushing themselves against the opponent, a series of continuous jabs more than one sole knockout alpha strike.   So, just as how we saw they are 'offensively defending', they are also 'defensively attacking'. Like waves, they constantly push themselves against their opponents, but always only inside their own cultural influence zone. This also means the Advent favor mobility, and will invest to field relatively larger fleets than their more stationary TEC counterparts. They specialize in strike craft and will typically field a large number of carriers, the ship type which makes maximum use of their guerilla 'wave' tactics.

Finally, there is a bias towards high-tech technology and research in general with the Advent: They have several technologies which speed the rate of their research. What this means is the Advent have a great deal of flexibility in their strategy: For instance, if the Advent commander deems enemy defenses are too strong to overwhelm, strategy can be switched into a purely defensive role where fewer ships are built and money directed towards research, rapidly scaling the tech tree in order to gain the upper hand.

Specializations: Culture, shields, research, strike craft

Advent Loyalists

Strategic doctrine: More defensively oriented than the Rebels, the Advent Loyalists are centered around two themes: Culture and revenge. The basic idea behind Loyalist play is to conquer through counterattacks rather than direct assaults - fight the opponent in own gravity well, use the Loyalists' superior defensive bonuses to defeat the enemy and force retreat, then pursue and overpower the opponent. Loyalist play is more deliberate than Rebel. The Loyalists will tend to rely on their more powerful culture to neutralize the enemy, waiting to lash out directly until the opponent has made his move.

Specializations: Culture, counterattacks

Advent Rebels

Strategic doctrine: The Rebels are more geared towards offense and direct assaults on enemy worlds than the Loyalists. They rely on fleets rather than static defenses to an even greater degree than Loyalists, expecting that the fight will be fought at the enemy's doorstep rather than their own. They will tend to field the relatively largest fleet of the factions mentioned yet. Their strategy is to overpower the opponent through sheer numbers, spending the least income on infrastructure buildup - instead, they rely on their faction's technologies to swiftly rebuild their fleet as well as the culture temples needed for further expansion into enemy territory.

Specializations: Offense, rapid buildup

Vasari

Strategic doctrine: The Vasari faction is the most aggressive, using the most offensive strategy and investing the most heavily into their fleet. That a great enemy is chasing very much shows itself in their style of play which centers itself on constantly progressing forward with little, but extremely rapid infrastructure buildup. The vast majority of income is invested into increasing fleet size in order to support the Vasari's nonstop onslaught. Supporting this offensive strategy, Vasari are heavily focused on mobility and detecting & dictating opponent's movements. They favour blitz or guerilla attacks rather than massed, prolonged battles and utilize their superior movement technologies to avoid these, taking combat to opponent's turf and hitting where it hurts the most. Again supporting this doctrine, their best weapon is long range missiles.

Specializations: Fleet size, mobility & movement control, missiles

Vasari Loyalists

Strategic doctrine:  Like their TEC counterparts, the Vasari Loyalists take factional doctrine to the extreme. They feature the highest degree of mobility in the game and are the least reliant on stationary defenses and bases. The Vasari Loyalists are all about maximizing fleet size as rapidly as possible - preferably including many capital ships - and laying waste to all opponents by first outmaneuvering them, then using brute force.

Specializations: Raw fleet strength, mobility

Vasari Rebels

Strategic doctrine: Unlike their isolationist, xenophobe Loyalist brethren, the Rebels are heavily geared towards diplomacy with most faction-specific technologies supporting cooperation with others. The Rebel commander will want to heavily invest into diplomacy and seek out alliances partners as early as possible. Against those that cannot be befriended the Rebels will apply the standard Vasari protocol of all-out attack. They aren't as powerful as the Loyalists, however, and will rely on their greater emphasis on and ability to conduct hit-and-run attacks. Against targets where such cladestine attacks aren't feasible, the Rebels will rely on assaults using the mobile starbase.

Specialization: Diplomacy, hit-and-run/covert operations