The first is that you're missing time as a frame of reference. Those two chains don't exist at the same time, and by the time the ring signatures chain reaches the level of transactions chain 1 has the lay of the land will be different. In other words, Bitcoin's blockchain right now is 20gb as it processes 61 000 transactions a day with a huge market cap and massive amounts of global reach. If Monero, for instance, reached that level in 5 years time it would have a 110gb blockchain by the middle of 2019. I have a 1tb Kingston thumb drive in my pocket, WD just released the 6tb version of their Red NAS series of drives. With HGST pushing HAMR drives for next year, they expect that in the next 5 years there will be 40tb - 60tb drives that are as readily available and cheap as 4tb - 6tb drives today. Will a 110gb blockchain on full nodes really matter by 2019, when everyone is sporting 40tb drives? By direct comparison: Bitcoin's blockchain takes up 0.5% of today's 4tb drives, and comparably Monero would take up 0.275% of 2019's 40tb drives. In other words, disk space and Internet capacity is rapidly outstripping potential blockchain growth.
Ring signatures provide cryptographically untraceable and unlinkable transactions for a small sacrifice in blockchain storage in a world where disk space is not at a premium.