I was a bit sad to see that the Vancian magic system carried over into 5E. I had my fingers crossed for a Magic Point system ala "Complete Psionics" or "Unearthed Arcana." But I digress.
The way I see it, there are three "frameworks" for spellcasters in 3E: the low-magic frame (ranger, paladin), the mid-magic frame (bard), and the high-magic frame (sorcerer, wizard.) Each can cast spells, but they have different limitations and focus.
Low-magic characters have a d8 Hit Dice and a high BAT, but they don't get spells until later levels, and they can only cast up to 4th level spells. Low-magic characters are more focused on martial combat than anything else, and they often have an interesting mix of extraordinary or supernatural abilities, but their magic-use is mostly utilitarian. They can cast spells in armor without a problem.
Mid-magic characters have a d6 HD, mid BAT, and they start the game with spellcasting ability, but their spell list is capped at 6th level. This character is more focused on skills than anything else, and the class has a lot of interesting special abilities, with a mix of attack and utility spells. They can cast spells in certain kinds of armor, which is somewhat limiting, but usually isn't a problem.
High-magic characters have a d4 HD and a low BAT, but they have access to magic at first level and their spell list is uncapped. Their focus is on spellcasting...they have fewer special abilities and class features, but their magic can do practically anything. Casting spells in armor is severely penalized.
Then we have the Cleric and Druid, and they do not fit any of these frames. It is almost like the designers cherry-picked the best parts of each frame and mashed them together...the special abilities and armored spellcasting of the low-magic frame, the mix of utility and attack spells of the mid-magic frame, and the early and uncapped magic use of the high-magic frame. I'm sure they had their reasons, but the end result was severely unbalanced.
To "fix" the cleric or druid in 5E, my advice would be to pick ONE of these three frames and stick with it. If you want clerics and druids to be combat-oriented, then keep the d8 HD and give them a high BAT but dial their spells way back (think "ranger" or "paladin.") If you want the focus of the class to be on skills and special abilities, then pull their HD back to d6, limit their armor, and cap their spells at 6th level. If you want the focus of the class to be on the spells, then drop their HD to d4, give them the lowest BAT, and cull their list of special abilities.
Or hell, do all three: give us a high-magic option (shaman, priest), a mid-magic option (druid, cleric), and a low-magic option (warden, warpriest) for each. Just resist the urge to mix and match. Trying to be all things to all spellcasters will only create balance issues. And nobody wants to see "Dungeons and Dragons V: CoDzilla Returns."