OK, here comes my post about the shifted balance in 5e. To understand those things, it’d be better if you played 3e, 4e or both, because about everything in this post will either take the one or the other edition into account.
If you compare your bonuses between those editions, 5e will see much less powerful. While you could almost everytime start with an ability of 18 (or 4e point-by/houseruled 20) and reached 28 without real trouble, the ability cap now is at 20 (except 20th level barbarian, which gets his ability and cap increased for strength and constitution) and your start more like 16-17.
While your start attack bonus from class starts higher than before (+2 instead +1/+0), you don’t get easy access to hit even more accurately or damage boost, so for most cases you’re stuck with ability&proficiency for hit and ability for damage at the start, unless you’re a fighter or a variant human. Afterwards it won’t get that much better for most, means that you won’t see a bonus of +14 or higher (without magical weapon or spell buff) at 7th level, more like +8.
Since the system is actually made to handle those lower bonuses, there is no reason to worry about game-balance. But since the bonuses are harder to get, magic items becomes much more powerful, since it’ll make a bigger difference, if you have a +1 weapon, if your final attack score without would be +11.
But responding to lower attack rolls, the AC of most monsters and even player characters got lower, too. But not only to response them, but even further, so while in 3e you tried to get not hit (which was easy, too) and 4e where you’ll have at least 1 almost unhittable defense if you’re decently careful, you’ll surely lose hit points in encounters and even worse: Since it’s hard to raise your AC, too, you might get overwhelmed by low-level monsters.
Logically speaking you shouldn’t be able to say, that you don’t have to worry about 100 normal goblins, since only 5 will hit you per round (in 4e sadly critically) as long as you have some levels. In 5e they’ll hit you on 18 if you have the unlikely AC 22, which is possible for some classes, so 15 will hit you per round, 5 of them critically.
Of course even in 3e or 4e you shouldn’t regard hit points, but even normal AC attacks got more serious, while most spells have a lesser damage output than in previous editions. Especially since your caster level doesn’t effect spells, only attack-cantrips gets stronger by having a higher character level.
In 5e you get less spells than in 3e, while most of them are initially stronger, but won’t be affected by the fact, that you got more levels, you need to cast them at a higher level or otherwise (like feats or class traits). And there are less ways to regain them at the moment, so every spell is more valuable, while the new system of preparing spells make place to prepare more spells that only might come in handy.
Further: Now any ability might make you a saving throw, even though the mains remain DEX, CON and WIS, any dumping stat could you make regret your decision. Since basically your only bonus will be proficiency, you will never really outgrow an enemy spellcaster, even a DC of 10 can be risky, if it falls to a non-proficient save. So you better don’t attack a temple of an evil god(dess) without serious preparation.
But even though 5e favors the weaker masses, you get some way to fight the masses better, like the base rule, that you can use your action between your move or can split up multiple attacks and moving freely.
Since bonuses are sparse, Advantages and Disadvantages are your best friends. Spells, traits and other ways to ensure Advantage for yourself or your party member, while imposing Disadvantage to your enemy will be more crucial and important during the game.
Another way are buffs to magic items or spells. Since most powerful buff-spells are concentration spells, the amount of possible buffs for one character will be often 1 per spellcaster.
So, you might ask, where is that shifted balance now? Everywhere. Instead of nice additions or ways to make one or two scores impossibly high, magic items are much more than just a bonus on a sheet of paper: You’ll feel their handiness. Instead of spell slinging damage, buffs, etc. every spell should be well thought, especially the concentrating ones and those you cast will have a great weight at that moment. Every trait which grants flat bonuses will be more worth, while there are less ways to actually get them. Instead of hording a lot of AC and complaining the fact, that your DM will hit you another way, you should be prepared to get hit regularly. And any dump will hit harder, since there are less ways to ignore them.
The balance shifted outside combat, too. The same procedure for skills, the fact that you can either choose an ability score improvement, which will come in handy at all situations or a feat, which will cover specific features (mainly combat). The fact that there is the Inspiration-Rule, which rewards good role-playing and some soft-bonuses from the background, which get much more work and love than in previous editions.
If I had to express the shifted balance in one sentences it’d be: Power-gamers, rules-lawyers and naggers be beware: Your pastime will be a lot harder!