TL;DR - While the Scarlet Witch may indeed be able to do more on her own than Dr. Strange, it's unclear that she normally has full access to that level of power. Lately, she's been portrayed as being a powerful witch (over and above her mutant powers), but not necessarily more powerful than Dr. Strange.
The Scarlet Witch's power has changed repeatedly, over the years.
Originally, her "hex power" simply involved the ability to alter probabilities in some random way, usually to her benefit. It generally took a few minutes for her power to "recharge" in the early days.
Over time, she gained better control of her power, sometimes being able to create a specific effect, and being able to cast "hexes" more frequently.
Eventually, she did begin to study magic (as noted in other answers) under Agatha Harkness (circa Avengers #128 et seq.). At this point, things begin to be less well-defined; it's not clear at any given moment whether she's using her mutant powers, magic, or some combination of both. It does seem like the combination of magic and mutant power was part of what allowed her to achieve specific effects with a hex.
A few years later, her powers were tied to Wundagore Mountain (where she was born) and to Ch'thon, who seemed to have some access to our dimension there. This increased the fogginess between her mutant abilities and magic, as a form of magic seemed to be tied into her mutant powers.
The nature of her abilities seemed to mostly remain constant for several years. in the late 1990s, they were tied to chaos magic (circa Avengers v3, #1-3). However, again, most of the time her powers seemed in line with the long-standing "probability altering mutant power, augmented/controlled by magic". Occasional stories indicated that she continued to study magic.
Her powers peaked in the 2000s, where she subconsciously decimated the Avengers (Avengers 500-503); then changed the world so mutants were in charge; then almost completely wiped out mutants (the House of M series/storyline); then wandered around not like an amnesiac; finally, undoing her "No more mutants" "spell". All of these events happened after she lost her children and went through the experience of having her husband, the Vision, de- and re-constructed, coming back without an emotional connection to her. In other words, for most of these events, she was not necessarily in her right mind. It's unclear if that state of mind allowed her greater access to her powers, or simply removed inhibitions she would normally have had against using them as she did.
When she regained her senses, she seemed to have difficulty undoing what she had done; reversing the whole "No more mutants" bit required assistance (Avengers: The Children's Crusade).
Her recent solo series (circa 2015-2016) established her as a member of the magickal community in good standing, and seems to indicate her magic abilities are at least approaching the level of Dr. Strange's; she's shown tracking down and resolving major magickal problems on her own.