From your post, I’m assuming the ease of the rotation is important, so I’ll focus on that. This is overly simplistic, but I hope it’s a useful overview. Generally speaking, mage is more challenging in my opinion, though not by any massive stretch.
Mage:
Arcane - Fairly challenging, but made easier in TWW. Still the most challenging as it requires specific timings that if missed ruin the DPS. Burn phase / Conserve / Mini-burn to rotate through.
Fire - Simpler than arcane but also reliant on hitting particular timings and has some nuanced tricks like jumping in combustion to better manage hot streak. Finickity. All about Combustion windows.
Frost - Straight forward, with a couple of procs/buffs to align. Comparable to Elemental in difficulty, generally speaking.
Shaman:
Lightning - very simple; Lightning Bolt generator, maintain Flame Shock dot, spend with Earth Shock. Use LvB before Earth Shock to buff. Storm Ele/Stormkeeper cooldowns.
Lava - maintain Flame Shock (usually with Primordial Wave), Lava Burst as main generator, spend on Elemental Blast. Use Icefury procs, fill with buffed Frost Shocks when Lava Burst is not available, and Lightning Bolt when buffed Frost Shocks are not available. Ascendence cooldown.
If your choice is between ele shaman or mage, I believe mage is the safest option.
The upside of playing a shaman is having the option to fill different roles, but if you are set on playing a caster, I do not see it being worth it to ignore the upside that mage has 3 caster specs.