I looked around a bit and found that WebSQL seems to be a little rocky right now.
On the one hand, it seems to have been widely regarded as a solution due to the fact that literally every actual implementation simply uses SQLite3, because the specification itself is heavily borrowed from SQLite3 design semantics, and it would be very difficult not to use SQLite3 specifically.
On the other hand, as of February 2017, all major browsers seem to support it ( http://caniuse.com/#search=websql ) - Chrome has it been presented for centuries, and it has been presented in IE11, Edge 14, Firefox 50, and Safari 10. Mobile phone support also seems to be positively positioned (right now there’s only a note that for some reason some Samsungs don’t work).
The theory behind IndexedDB makes sense: it is a completely new standard, not tied to any existing library, and manufacturers can create their own implementations, create competition and avoid blocking the provider / library. However, I crashed into one of the most negative aspects of IndexedDB: its abstract design seems to have absolutely disastrous performance due to implementation overhead.
http://scaljeri.imtqy.com/indexeddb-vs-websql/v2.0.0/index.html is an interception of IndexedDB-vs-WebSQL with one click. I set it to 10,000 points (a rather modest number) and gave it a try for my ThinkPad T43 - a single-core 2 GHz Pentium M with 2 GB of RAM.
First of all, nothing but Chromium running, most tabs are paused, and the rest of the tabs do not use any processor:

Throughout the whole time, "Paste" on IndexedDB on the tab used 100% CPU, and the system is generally unusable. (I could get around - screen shielding was just very slow, but I didn’t do it for an accurate test).
I also had to play with the tab when I had many other things, and the system, as it turned out, changed to death (something very often happens on this particular machine):

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