They are two irrelevant processes.
On Ubuntu, all system files has already been scattered around the disk.
Thus, by using a SSD, you get a significant performance boost due to the reading speed.
On TC, however, the files are compressed in packages (tcz).
When TC boots, they are decompressed and mounted as loop devices.
In case you're running in COPY2FS mode, the files are decompressed then copied to the ram.
Either way, the boot time depends on the amount of files you're loading and the speed of your processor.
So, to answer your question
What can I do to get boot speeds that beat Ubuntu?
Well, boot TC with bootcode
base norestore.
Or overclock your computer. (thought I doubt it would make much difference)
Please take the time and read
this document or
the book to understand the philosophies behind Tiny Core.