Yes, there are adapters with full function (the pretty expensive Metabones adapter springs to mind) so you'll have aperture control, but the AF performance won't be anything near what you're used to on EOS mount. To quote from their website for the Mk III EOS->E adapter:
Autofocus is supported, with the following known limitations.
Autofocus speed is very slow and inadequate for most moving subjects.
The autofocus speed is unfit for professional use for sure, and it
would disappoint most enthusiasts. Only Canon-branded lenses
introduced in or after 2006 are officially supported. Autofocus may be
disabled for older Canon lenses and most third-party lenses, including
most Sigma, Tamron and Tokina lenses and all Contax N lenses modified
by Conurus. ...
Along with a whole mess of other caveats. So, practical upshot, you'd probably be better off trying to adapt manual-focus lenses that have an aperture ring on them. Much simpler, easier, and pretty much the same (or more) function. And if they're rangefinder lenses, then the size/weight is closer to ideal.
In the mirrorless world, to me if you're a Canon L shooter, if you're willing to sacrifice sensor size for lens selection, you go µ4/3. If you're happy to sacrifice lens selection (and speeed) for full-frame, you go Sony A7 system. And if you're happy with APS-C and fast expensive glass, then you go Fuji X.
The Sony A7 models are particularly problematic, given how there's a lack of full-frame lenses for it from Sony, they tend to be very expensive, and adapted rangefinder lenses--particularly the Leica M wide angles, have questionable performance, quite possibly due to the sensor stack thickness. In addition, to keep size and weight down, most of the full-frame E lenses are f/4, but have f/2.8 L lens prices. Best to make your peace with that before getting an A7, in my book.