If you want to have rare but powerful magic, just limit the number of auras, raw vis, creatures, and magi (Hermetic wizards) and members of other supernatural traditions.
If you want to have magic be weaker, it's more tricky. I'd suggest doing away with playing Hermetic magi. Play Companions instead, with Supernatural Abilities (not the full-blown magical traditions depicted in the Hedge Magic Revised Edition book, for example - these tend to be too powerful), perhaps organized in some Mystery Cults (which will allow greater opportunity for character development and furnish the setting with cults you can throw at players). Use spell-like vis and enhanced items of virtue (from Realms of Power: Magic); these allow you to make use of colorful "magical items". You may use the "natural philosophy" rules from Art & Academe if you want to give an authentic-feel to supernatural medicine, alchemy and divination, but this may make magic too common for you. You may want to read City & Guild too, to get more setting information, especially if you're interested in commerce and craft. Hermetic magi can still be around, but as rare background NPCs, as setting-elements instead of PCs.
The result is a setting that is very weak-magic, with characters relying on their magical lore and magical items, plus perhaps a supernatural ability per character, to deal with the Monster of the Month (a faerie trickster, Machiavellian demon, magical beast, or so on) - or with whatever you choose to throw at them.
I find the most problematic part of the setting is the power-level of Hermetic magic. If you lower it (as discussed above) or eliminate magi (as I suggest above), the setting becomes very coherent and the rules work well.
The only remaining major-incoherence in the setting is the unity of the Divine - only one Divine Realm/God, with a united host of angels, yet a multitude of conflicting and even warring religions. This is a problem for any setting that wishes to protray a supernatural-version of historical Europe, and Ars Magica deals with it as well as can be asked in my opinion, by choosing the "God works in mysterious ways" option; you will have to decide if this works for you, or you prefer some other approach.
I'm not sure which fantastical elements you want to incorporate. Be mindful that Ars Magica treats some of them in ways you may not expect. They work well, in my opinion, but you may want to take that into account in advance.
Notice that Faeries in Fifth Edition are weird creatures that live off the "Vitality" of humans; and "vitality" can mean almost anything, from freely-given hair to worship. This includes most pagan gods, that lived off the worship of humans. If you wish to include Titanomachia fantasy in your saga, this is treated as Faerie-gods binding the Magical-titans and thus harvesting their power.
The faerie idea of drawing vitality can be easily extended to all manner of creatures, such as vampires or Earthdawn-like "Horrors" that live off fear. It also includes some "standard" faerie creatures such as brownies that work for milk, but notice that it does not include other "standard" faerie creatures such as wood-spirits (which are Magical creatures, not Faerie).
Another major point is that demons in (standard) Ars Magica Fifth Edition are really different, psychologically, as they are creatures "without Virtue" (with no temperance, bravery, or so on). They make for very malign creatures that are utterly evil and powerful, but also deeply flawed. They are generally more interested in collecting souls for hell than in killing people, and in causing their own preferred kind of suffering/vice and playing their own evil games for their own amusement.
The rest is pretty normal. Dragons, good-natured angels spurring humanity forward, and so on.