Akali or Kat Mid-Lane

as a bursty mid lane mage?

Akali isn't a mage in any sense of the word, she's more assassin than most assassins. She's all about mobility, stealth, and single target DPS.

Katarina being more AoE than anything else ever can land her in a spot where she's arguably more mage than assassin though.

As for pros and cons? Both are pretty weak per-6. Akali can do some work on anyone who trys to take her on in melee range, but usually smart opponents won't let you get close. Akali can wave-clear and last hit OK for being a melee champion, but isn't particularly amazing at doing either.

Katarina is so heavily reliant on her ultimate a lot of champions that clearly outrange her can also win a face-tank fight against her (pre 6), which is a fairly odd pattern within LoL, as range and damage potential often scale against one-another, allowing shorter ranged champions a chance at winning 1v1 lane match-ups by finding an opening to go ham. That said - Katarina doesn't even have to manage energy and her wave clear potential is pretty solid all things considered. Well-timed Bouncing Blades also have the potential to strike opponents from unusually long distances, so if Katarina plays her cards right she can win endurance games against her opponents and poke out champions that should be poking her down.

Post-6, Akali is a pretty solid assassin. She doesn't have quite the mobility or skilled play potential as Zed, but she can face-roll most unfortunate enough to find themselves in a 1v1 against her. I've seen her go Legendary more than any other champion when I started playing Dominion as well, as Akali is brutal against players that don't know how to deal with her. Her Cons though? Ridiculously easy to counterbuild. A pink ward shuts down a lot of power from her kit. Some argue that spending 100 gold to deal with a champion is a 100 gold tax. Those players are misinformed, there aren't any 100 gold options to let you target Fizz during Playful/Trickster or AA Jax during counterstrike. Also - Akali is so much magic damage even her auto-attacks deal magic damage, which is bad news bears if you ever run into a fighter with things like Wit's End and Hexdrinker, because they'll take a dump in your bowl of cheerios.

Post-6 Katarina is rather different. Katarina doesn't fare as well in 1v1 situations as most assassins. Or most champions in general - mages like Annie can pull off some solid plays if they're spread out at ~100 second intervals. Katarina functions ideally in ~3v3 situations. Due to her ultimate being canceled by Zhonya's she doesn't bring as much team-AoE power as a solid number of other AoE squish focused on hurling themselves in the middle of the enemy team, but with her re-sets and mobility she does very well in skirmish after skirmish after skirmish situations, or just against a team that's a little split up when a fight starts. That ~3v3 situation is actually pretty common - with roaming to top or bottom lane, especially when trying to capitalize on counter-ganks, Katarina can really shine. She's one of the strongest mid-lanners in regards to roaming potential and aiding top or bot lane, and she's got some mobility to help her reach those lanes as well.

Katarina's ult damage is pooped on to a certain extent by the vast majority of CC effects in the game, but with it's minimal channel time (and most CC effects having fairly lengthy channel times and slow projectile speeds) you're still likely to get off a solid chunk of damage against players that are trying to react to you. The biggest issue with CC is the clever players that anticipate where you're going to go. End-game with DFG you only really need ~1 second to melt a squish, which is about the time it takes CC-heavy supports like Leona to just cast Zenith Blade.

I personally prefer akali but both have their ups and downs Akali: good: huge single target burst, very few counters mid, can chase extremely well due to 3 ults, gets another ult cool down with kill Bad: AOE champions can cause problems for her in her shroud, cc can cause big issues for her, not the greatest escape, one multi target attack Katarina: Good: AOE ult does major damage in teamfights, huge burst, can get in and out of fights quite easily, resets on cool downs Bad: can be counter picked fairly easily, ult can be cancelled by anyone with a stun, root, or knock back/up, if not fed has issues, can be caught up by cc

Both have the ability to snowball very well but akali I find can be harder to lock down with her shroud and is always moving unlike kat who has to stay right in the middle of the team fight and will be focused and quickly killed by people who know what they're doing