They've sort of baked in Prestige Classes into the base classes, you choose a specialization for your class, so all characters get a little extra twist to them.
So your fighter at level 3 could choose the Eldritch Knight Martial Archetype and get some spells and abilities that would give you some bonuses and not sacrificing BAB. In 5e armor is much more powerful aswell since you don't have Touch AC just plain AC, so your Ranged Attack spells are harder to land on a pondering Fighter in full plate than that naked nimble thief.
If you play a Bard you can choose to focus on melee via Bards College of Valor or spells and skills through College of Lore, and there are a few more. Clerics and Wizards get domains and spell school specialization instead.
Technically speaking since BAB is based on your Proficiency bonus, a Wizard and Fighter has the same BAB, so if you pick feats you can be a decent swordsman aswell. The fighter has alot more HP (D10 instead of D6) and more Features from their class.
Rambling on; If you really want to break the game you play as a Valor Bard, choose some Paladin spells as your bonus spells and you're set to go. Bards get to choose a couple of spells from other classes spell lists and Paladin/Ranger spells are really powerful for their levels since they're normally accessed at much higher levels since they get slots half as quick as full casters, so their most powerful 5th slot spells normally accessed at level 17 the bard can get access to at level 10 and can cast at higher spell slots. Borked.
Or just go for a Drood, Circle of the Moon can wildshape into higher Challenge Rating monsters than normal and recover Wild Shapes with every 1hour rest, meaning you can soak ludicrous amounts of HP will still doing damage and if push comes to shove you can spend spell slots to heal your wildshape HP.
Anyway, there are some options to get a little variation with the class specializations, but you will not get a massive bonus for doing so, and actually penalized if you're an innate caster. Cantrip spell damage scales with Caster Level rather than slot though, and cantrips will be one of your most oft used spells, so they've got some multiclass protection in there aswell. The higher level class features are really powerful and since you're multiclassing, well, wave all those goodbye.
I personally prefer 3.5e to 5e, the other GM and players prefers 5e since the rules have been streamlined.