Contagion is insignificant as magic damage is the lowest source of damage in most fights. With one caster, and 2 healers your buffing on average maybe 800 dps each from the healers, and the caster. With Embolden, You buff both tanks, the Red Mage, and every other physical dps. Trick attack buffs all damage by 10% for 10 seconds. Embolden only drops below 8% physical damage after 8 seconds. Brotherhood is a 5% physical dps that lasts for 15 seconds, and Embolden only drops under 6% after 12 seconds. For contagion to be as good as Embolden, it would either have to last longer, be a larger increase or include all damage.
Even if you are running a comp with 2 healers 2 casters 2 melee and 2 tanks, embolden still would be better as it buffs the red mage, both melee and the tanks. (Over half the group, and the most damage dealing member's of the party)
Synergy wise, Summoner isn't as friendly to the one caster Meta as Red Mage. You can switch between both pets to get radiant shield and contagion, but at the cost of mana to switch your pets. and at reduced personal dps from using your mana. Red Mage is more complex in summoner when it comes to positioning and movement. Rotation wise, they are about as equally complex when you factor in RNG and when Red Mage will get their melee combo. Summoner can just ruin 2 when they need to move, and you can hold or pop deathflare whenever you want without issue. While when I play Red Mage, I only have bursts of movement, and need to juggle movement and casting.
https://www.youtube.com/watch?v=07Id6TH72Qk
