I want to start to examine Blue Book D&D and see where it differs from B/X D&D with the Moldvay set. I'll start with Magic-User spells, since they have some meaty differences.
Holmes has several more spells. At first level, Dancing Lights and Enlargement are added to the list. At second level, we gain Audible Glamer, Darkness (a reverse Light), Magic Mouth, Pyrotechnics, Ray of Enfeeblement, and Strength. Also, Tenser's Floating Disc uses Tenser's name in Holmes where it doesn't in Moldvay.
Charm Person is much more powerful in Holmes, because the ranges wind up being longer for most Intelligence scores. Light in Holmes lacks specific rules about being cast at a creature's eyes, leaving this as a ruling for the referee to make. Magic Missile is superficially worse because it needs a roll to hit. But Holmes only wrote "Higher level magic-users fire more than one missile," and it's never expanded on in the Cook/Marsh Expert set, so the spell could allow more missiles than in Greyhawk and Moldvay. So a house rule that would make the spell more useful would be one missile for every three levels beyond first, getting your second missile at 4th level - and making it a pretty useful spell at higher levels.
Protection from Evil has the same function in Holmes and Moldvay, but in Holmes it's a better spell because it doesn't explicitly break if the caster attacks a monster. Read Magic lasts two turns instead of one turn. Sleep works differently in Moldvay than Holmes. In Holmes, if creatures are up to 1+1 HD, then 2d8 creatures are put to sleep; if they are up to 2+1 HD, it's 2d6 creatures; if they are up to 3+1 HD, 1d6 creatures, and for 4+1 HD, only one creature is put to sleep. In Moldvay there are 2d8 hit dice worth of creatures unless the creature is 4+1 HD, in which case it is only one. The probabilities work out fairly similar and Moldvay's way is simpler, but Holmes's has the OD&D pedigree.
Continual Light is the same as Light in both versions, with the same addition in Moldvay. Holmes is less philosophical about evil for Detect Evil, presumably because that edition actually has an evil alignment - although it still is detecting "evil thought or evil intent," not alignment as such. Interestingly Moldvay adds traps to poison as not being evil. There aren't a lot of restrictions on ESP in Holmes about concentrating a full turn or getting thoughts jumbled up, but otherwise the spells work the same, so it's simpler for Holmes.
Invisibility in Holmes is again better - you can cast a spell without breaking it, so long as you don't "strike a blow." Clearly the referee has some leeway on this, but by default it's not as restrictive. In Holmes, Levitate can be cast on another character, while in Moldvay it can't. Motion in Holmes is also 60' per turn up, where in Moldvay it's only 20' up or down. Mirror Image is one of the few spells that got better in Moldvay, where it specifies that an attack on the caster always hits an image instead. Holmes has no such stipulation, just that each image disappears if hit.
Holmes's Phantasmal Forces is the magnificent spell from OD&D, which does real damage if it is believed, and has none of the saving throw jibber-jabber, although a living creature touching it will dispel it. Web works about the same in both Holmes and Moldvay but covers twice the area (10'x10'x20' instead of 10'x10'x10') - not coincidentally that should be two dungeon blocks on a 10' map instead of one.
From a spellcaster's perspective, Holmes (which frequently follows the LBBs although often adding bits and pieces to them) offers mostly stronger spells than Moldvay. In Moldvay there is more of a tendency to spell out exact consequences, which in my opinion really takes spells like Phantasmal Force(s) down in overall power. Between the scroll rules, the spell descriptions and the spell learning rules, Holmes makes magic-users a bit more powerful.
The thing I really enjoy about Holmes versus Moldvay is that Holmes was more reserved in his spell descriptions. This leaves a lot more room for player and referee creativity and interpretation. The wide-open nature of Phantasmal Forces versus its relatively tame Moldvay version is probably the most dramatic example, but Invisibility which I see as one of the most powerful M-U spells for a dungeon exploration game is also much more wide open.