Thanks for being curious. I scraped around to find some numbers to back up my wild claim--I think I did a fairly decent job of it. I do warn you--my numbers are pretty rough.
Blockchain.info claims to be the most popular web wallet with 10M users and users have control of their own keys without needing to run a node. Their android app has 1-5M downloads.
The Mycelium wallet for android has 100k-500k downloads.This is an SPV wallet like electrum, where users have control of their keys without needing to run a node.
Bitpay's wallet for android also has 100k-500k downloads, which is an SPV wallet.
The generic bitcoin wallet for android (also SPV) has 1-5M installs.
Multibit (also SPV) is the only desktop client that posts statistics but it claimed 1.5 million downloads in 2014. Now that multibit is discontinued (and bitcoin has gotten more popular since 2014) it's fairly safe to assume that electrum has numbers quite a bit higher than that. I suspect (although I can't prove) that electrum is more popular than all of the android wallets--It's even packaged in TAILS by default.
For comparison, the only popular wallet where users DON'T have control of their keys is the coinbase wallet with 9 million accounts. Other exchanges exist, and may have higher volume, but they don't market themselves as wallets to users.
There are less than 10,000 full nodes running at any given time--and a large amount of that is running 24/7. Its safe to say full-chainers are in the minority if you do some guesstimation.
I got most of these figures from the google play store.