there is no way of knowing this because first of all we don't know how many bitcoin users are. secondly these wallets don't leave a trace for example when you use Electrum and send a transaction all the world sees is your transaction and it is the same thing as when you use bitcoin core, Armory, blockchain.info,...
based on what i have seen, most new users are either using Coinbase or blockchain.info. something like 80% of the newcomers.
there is also number of nodes which show how many are using core as their wallet
https://bitnodes.earn.com/nodes/ it is about 10k reachable nodes but also there are a lot more which are only receiving but not accepting incoming connections.
another method can be asking for stats on number of downloads of each wallets. this may not be accurate but it is good enough but for that you need the stats from each website. for example from Electrum.org and its github page. this is not publicly available!!