In general, Trails of Cold Steel gives you more leeway with which to build your characters. In Trails in the Sky, your characters had set stats which dictated how you would ultimately build that character. Zin would always be built as a heavy tank, with HP, DEF and ATK quartz, the only variation being how much you balanced between attack and defense. Kloe would always be the team healer. Olivier had a gun, but it was always optimial to build him as a nuker, increasing his magic attack and reducing cast times. Outside of a handful of exceptions like Estelle, you'd build every character the same way on every playthrough.
Trails of Cold Steel has fixed this, where the bulk of a party member's stats have been transferred to the Master Quartz they wield, and since MQs are interchangeable, you can now redistribute the stat balance of your characters and therefore, fundamentally change the playstyle of that character. The MQ's have their own effects helps too. For example, I could have Fie and build her several different ways. Did I want her to be a straight up speedy attacker? Sure, slot in Raven, stack attack quartz and speeds quartz and volia. Did I want her to be spellblade? Load up Pandora or Ciminal and stack golden quartz. Want her to be a tank? You can make her a straight up dodge tank with Falco, Evergreens and evasion quartz, or give her some sustainability with Thor's and life-stealing quartz. Do I want her to spread status conditions everywhere? Stack DoT (damage over time) and crowd control effects and spam Speed Cyclone. Never before in a Trails game, have you had so many options with which to build your characters.
Here are some of the builds I had success with
Rean
+ High damage per battle
+ Evasion tank, ideal for counter build
+ Fast
+ Status inflicter (thanks to his AoE crafts)
+ Dealyer (Arc slash particularly)
- Low arts potential
MQs: Chevalier (draw aggro) or Vermillion (double damage).
Items: Gladiator headband, Medal of Dawn, Evergreen
With the Chevalier, 50% evade, insight, and the Gladiator Headband, Rean was attracting the attention of everybody, countering their attacks, and building up CP for an ultimate incredibly fast.
Vermilion, evasion tank Rean is the best damage dealer in the game. With 1500 attack at end game, he will annihilate everything, including anyone who dares try to attack him. His ultimate hits the final boss for 33k damage.
Gaius
+ Evasion tank, ideal for counter build. Having a spear helps too.
+ Status inflicter (thanks to his AoE crafts)
- Low arts potential
- Otherwise average stats
MQs: Falco, Thor, or Chevalier
For Chevalier, run the same build as Chev Rean.
Thor and Falco are self explanatory. Falco gives you 5 turns of insight (50% evasion, ontop of his 50% evasion for guarenteed evades and counters) from the get go, while Thor requires you to spend a turn to cast insight. Thor gives you more health and lifesteal though.
Laura
+ Highest raw damage per turn
+ Tank (highest health of all characters)
- Slow
- Terrible arts potential
MQs: Brave, Tauros, Thor, or Chevalier
Items: Medal of Friendships, Salmon Badge
Laura is self explanatory; dump Force, Tauros, or Vermilion on her and raise the attack stat for super damage (note that in the first game, Tauros does NOT double the damage of crafts). If you are using Tauros, be sure to use the time acceleration art and raise her speed stat.
Chevalier and Thor are two different methods of tanking; Chevalier draws aggro and makes her the ideal tank (rocking 15k health and 1200 defense at endgame), while Thor gives her a boost to damage and lifesteal to recover health.
Alisa
+ Ranged
+ Support (provides team with CP)
+ Heal support
+ Great ATS
- Terrible physical damage
- Squishy
MQs: Moebius, Criminal, Canon
Items: Gladiator belt
Alisa is best used as a support character. I put Moebius on her and emphasized her speed and range. My modus operandi was to have her cast CP regen on the team, buff/debuff with Chrono Drive/Chrono Break, and chuck food onto everyone. Alternatively, you can take advantage of her ATS and make her some sort of caster, either dealing damage or healing the team.
Jusis
+ Top tier STR and ATS
+ High magical potential (can become a caster)
+ Fast
MQs: Orochi for physical damage, or whatever casting MQ you want
Items: Medal of Dawn
Jusis can be built along a range, from a straight up attacker, to a balanced spellsword, to a fullblown caster. My straight up attacker Jusis was rocking 1400 attack, and with Criminal he can become the most powerful mage on the team. He's basically Olivier if his physical damage was actually practical.
Machias
+ Strong AoE damage (ideal for spreading status conditions)
+ Highest HP and DEF (second to Laura)
MQs: Brave (buff your AoE damage), Megalith, Chevalier (become a fullblown tank), Thor (Recoup tons of health from your AoE damage), Force, Tauros, or Moebius.
Items: Gladiator Headband, Medal of Dawn
Machais is blessed with tankiness and the ability to slaughter groups of enemies with his shotgun, giving him tons of range. You can stick Moebius and buff/debuff arts on him and allow him to run support; you can make him a tank, or you can make him into your group slaughtering machine.
Fie
+ Great STR
+ Evasion tank, ideal for counter build
+ Fast
+ Status inflicter (thanks to his AoE crafts)
+ Magical affinity
- Squishy
MQs: Thor or Falco
Items: Gladiator headband, evergreen, passionate rouge
As I previously said, Fie's got so much range. She can evasion tank, spread status conditions with her high speed and AoE, delay the enemy team, become a versatile spellblade, etc.
Elliot and Emma
*The only characters who got shafted*
+ High ATS
- squishy
- staff weapon
- Terrible STR
While the MQ system worked wonders for Falcom's attempt to give each character a wide range of options, it can't make up for the ingrained fact that Elliot and Emma wield the worst weapon in the game. With staves being based on STR, and Elliot and Emma having terrible STR (not to mention being too squishy to survive a melee), they are ultimately relegated to caster roles, either as a healer, an arts support, or a straight up nuker.