Not sure how missions have changed, I haven't played in about 1/2 a year.
But missions to ships tended to be:
lvl 1 - easy in frigate
lvl 2 - very tough in frigate but some missions doable (cruiser recommended, battlecruiser very easy)
lvl 3 - battlecruiser struggles on some missions (some exections ie. drake is a walk in park), heavy assault ships easy
lvl 4 - battleship recommended
It all really depends on which race of ship you fly too and the damage types you do and resistances you have vs the npcs. I flew Amarr and the above is what ratio I would apply to Amarr/Gallente/Minmatar but Caldari will probably find missions easier, so you may get away with trying harder missions in a smaller class ship.
Best bet is to check the mission guide sites to see what difficulty they rate and then you can judge as to whether you might be able to do a higher lvl misssion (Be aware they go out of date regularly):
http://eve-survival.org/wikka.php?wakka=MissionReports