Advantage 1: More possible spells
Primary advantage of the Ring of Spell Knowledge over the Page is that it lets you cast spells not on your class list.
A ring of spell knowledge is only a storage space; the wearer must still encounter a written, active, or cast version of the spell and succeed at a DC 20 Spellcraft check to teach the spell to the ring. Thereafter, the arcane spellcaster may cast the spell as though she knew the spell and it appeared on her class’ spell list.
Emphasis mine. RAW, it allows any spell, even those usually restricted to divine casters. When casting it yourself, it will be considered an arcane spell regardless of where you got it.
Advantage 2: Switching out spells
An important advantage of the ring is that you can switch out the spells. Just have a stack of scrolls, and you can switch the spell out at will. Scrolls don't get consumed when doing this.
If you have other spellcasters in your party, they could also cast them for you to put into the ring, and you can Take 10 on that DC 20 Spellcraft check. As Intelligence isn't a stat spontaneous spellcasters usually invest in, this may require some skill ranks to get reliably right in a single casting.
Disadvantage 1: Off-class arcane spells are penalized
Arcane spells that do not appear on the wearer’s class list are treated as one level higher for all purposes (storage and casting).
This doesn't affect stored divine spells. Not much to say about it, honestly. This might cause you to seek out divine versions of those spells if available to a divine class.
Disadvantage 2: Level is capped.
The highest available ring in RAW is level 4. Period. GM's may be willing to allow higher rings, but you can't count on that.
RAW, you'd need a level 3 ring to store cantrips:
A ring of spell knowledge I can hold 1st-level spells only, a ring of spell knowledge II 1st- or 2nd-level spells, a ring of spell knowledge III spells of 3rd level or lower, and a ring of spell knowledge IV up to 4th-level spells.
But I honestly can't imagine why a GM wouldn't let you put it in a level 1 ring. And you probably have a LOT more important uses for a ring slot than paying 13 500 gold to gain access to a single cantrip.
RAW, divine spells are allowed into the ring. There is some discussion on some forums about whether divine spells could be allowed, but no official word as far as I could find.
The most common argument against I found was "well, obviously".
I think it is intended to allow this on purpose. Otherwise, the combination of taking a slot AND being more expensive doesn't make sense with Paizo's own design philosophy. Normally slotless items cost double. Accounting for that, the Ring is three times as expensive as a Page. Just switching out spells doesn't make up for that huge disparity. Those few arcane spells not on your list aren't that gamechanging either. But access to normally divine spells like Cure Critical Wounds or Restoration is worth it.
I suspect that the allowance of divine spells is also the reason that the maximum level for a ring is limited. Otherwise putting Raise Dead in the Ring becomes an option, which might be encroaching on the divine caster territory a bit much.
Still, you might want to ask your GM for an explicit ruling about how it will be treated on your table.
Advantage 1: Slotless
Primary advantage of the Page is that you can hold unlimited of them. No downsides.
Advantage 2: Accessibility
If you have Craft Wondrous Item, can just make them yourself. You will take a +5 to craft DC for not knowing the spell. This also halves the cost compared to having to buy them.
Advantage 3: Divine Spontaneous Casters
The page can be used by divine spontaneous casters. Obviously, if the Ring is an option, this isn't an advantage for you. But it's worth a mention for all those Oracles out there looking to broaden their understanding.
Disadvantage 1: Smaller spell pool
Pages only work if the spell is on your class' spell list to begin with. "knowing" a spell doesn't do anything for you if you don't have it there. This means that a Sorcerer cannot learn Cure Light Wounds this way, even if another arcane caster (like a bard) crafted the page with that spell.
Disadvantage 2: Expensive
Page cost adds up fast, especially on higher levels. Assuming you craft them yourself, the 500 and 2000 gold for levels 1 and 2 are doable, but costs increase fast. 40 500 gold for a level 9 spell is expensive.
Disadvantage 3: No cantrips
RAW, there's no provision that lets you put a cantrip into a Page of Spell Knowledge. But I'm confident most would let you either make one for the price of a level 1 spell, or even for just 250 gp, which the quadratic formula would give for a level 1/2 spell. (often used for item creation with spell level 0)