I found a pretty exact way to answer this question. It exploits the sentinelsat Python API to extract the desired information directly from ESA's SciHub:
from sentinelsat import SentinelAPI
api = SentinelAPI('yourUsername','yourPassword')
S1 = api.query(date=('2017-01-01T00:00:00Z','2017-12-31T23:59:59Z'),platformname='Sentinel-1',producttype='SLC',sensoroperationalmode='IW')
S2 = api.query(date=('2017-01-01T00:00:00Z','2017-12-31T23:59:59Z'),platformname='Sentinel-2',producttype='S2MSI1C')
This gives you 2.07 Petabyte of Sentinel-1 IW SLC data (ignoring GRD data, which was derived from the SLC data, as well as ignoring the non-standard acquisition modes). It would also give you the Sentinel-2 Level-1C data (ignoring Level-2A data and other non-standard products), but I currently don't have time for the data catalogue being downloaded. Nevertheless, I consider this a pretty good estimate for the annually produced data volume. If one has a different definition of annually produced data volume, it's easily possible to use different search parameters or no search parameters besides platformname at all.
EDIT: I finished the check now and want to include it to the answer for sake of completeness: Apparently, for 2017 there are 0.94 PetaByte of Sentinel-2 L1C data in the archive. Thus, one year's worth of standard Sentinel-1/Sentinel-2 data can be estimated to take about 3 PetaByte of storage.