Yes and No
Grappling in 5e is very different from 3.5e but for a character customised for it, much more powerful. I refer you to the Grappler's Manual.
A character (or beast for those who polymorph before grappling - the T. Rex is an awesome grappler) with proficiency or, even better, expertise in Athletics is going to win 90% of grappling checks over a creature, even a strong or dexterous creature who doesn't.
Starting the grapple is step 1. Step 2 is knocking the opponent prone:
A prone creature’s only movement option is to crawl,
unless it stands up and thereby ends the condition.
The creature has disadvantage on attack rolls.
An attack roll against the creature has advantage
if the attacker is within 5 feet of the creature.
Otherwise, the attack roll has disadvantage.
If you take the Shield Master feat you can do step 2 as a bonus action - its much better than the Grappler feat. In fact, the Grappler feat sucks, it takes away the best thing about being a grappler: your mobility.
You give yourself (and any of your companions within 5 feet) advantage on attacks, give them disadvantage on attacks and lock them in melee because "Standing up takes more effort; doing so costs an amount of movement equal to half your speed" except they don't have any movement so the can't stand up. They can either fight at disadvantage against your advantage or waste all their actions trying to break free - which they won't do because you have Strength (Athletics) at +11 against their feeble +4.
Throw in some nice environmental effects like dragging them to the edge of a cliff and throwing them off, holding them in the fire or underwater, or jumping up and throwing them to the ground, or spell effects like holding them in a Sorcerer's Wall of Fire or a Cleric's Spirit Guardians and you can see how awesome this is.
Did I mention that because you have 2 hands you can do this to 2 creatures at once?
A recent encounter of a party I DM for against an adult Green Dragon illustrates:
- The Barbarian/Rogue with expertise in Athletics (proficiency doubled to +8) is raging so has resistance to the dragon's natural attacks.
- The Bard Polymorphs the Barbarian into a T. Rex (Strengh +7) - Strength (Athletics) +15. The dragon has no proficieny in Athletics or Acrobatics so is relying on its raw strength modifier or +6. The bard then ducks out of the dragon's sight to maintain concentration.
- This give the T. Rex barbarian an 85.25% chance of initiating a grapple (twice due to Extra Attack) and the dragon a measly 11.25% chance of breaking it.
- The Sorcerer casts Wall of Fire which the Barbarian holds the dragon in
- The Cleric cast Spirit Guardians which kept tearing at the dragon
- The dragon used its breath weapon as often as possible and attacked as much as it could but it missed a lot with the disadvantage. Anyway a T. Rex has 136 hp and a raging barbarian is resistant to the dragon's non-breath attacks.
- The dragon got away once due to its Suggestion legendary action but what with getting up from prone and Disengaging the T. Rex caught it and dragged it back to the fire.