assassins are generally burst, but always single target damagers. They're whole purpose is dropping one person (usually the opposing carry) as soon as a fight starts, then getting the fuck out of dodge.

Tryndamere can carry, but he's easily shut down at higher ELO levels. In order to work effectively, he needs a full page of crit CHANCE (not dmg) runes to work his healing in the early game. While he is fantastic 1v1, this loses effectiveness once the game has gone on long enough. His ult gives him 6 seconds of invincibility (and free crit chance), but what happens when you're ignited halfway through? popping bloodlust will sometimes save you, but most (competent) teams will anticipate tryn ults and straight up stun you partway through and ignite.

Early game, he is easily zoned out in lane by pretty much any ranged attacker. His heal relies on getting crits, which means you need to be around the creepwave or the enemy. Getting harassed constantly without being able to reliably crit is a recipe to you getting underlevelled and underfarmed when Tryn is heavily, heavily reliant on items. inf edge and PD alone come to almost 7000 gold. throw in boots and that's an entire game's worth of farming, generally speaking, and this doesn't give you any aspect of survivability like lifesteal, armor, health etc.

tryndamere, in my experience, is most effective as an assassin. When a teamfight breaks out, you spinning slash out of the brush or across a wall kill, ashe in 3-5 hits, pop your ult so you don't die and slash away again. Anyone who deals the amount of damage tryndamere does and with the low amount of hps he has becomes a huge target, even with a 6s invincibility ult. you'll get bursted in a heartbeat and you desperately need to avoid snares/stuns and DoTs. playing tryn against opponents who are familiar with the game is difficult to do.