What is different between fixed-size disk pages and disk-based?
What Stonebraker is talking about here is essentially his latest baby, VoltDB. This is what Stonebraker (a huge hitter in the database world) calls "NewSQL". 

He says that OldSQL (The Oracles, MySQLs, SQL Servers &amp;c. of this world) waste too much of their resources Logging, Latching, Locking and on Buffer Management. These result (largely) from the fact that the data moves back and forth between disk and memory as transactions are processed.

He also says that NoSQL throws the baby out with the bathwater in that it gets rid of something he regards as critical for any database system worthy of the name, i.e. ACID transactions.

He sees VoltDB (and similar NewSQL) as the future of OLTP database systems - this is an in-memory shared-nothing system where transactions are in the form of app-specific customised stored procedures which always run to completion. This architecture eliminates all the logging, latching, locking and buffer management that Stonebraker says is essentially useless work. He famously said that OldSQL should go to the home for "tired software"! You might want to check out this paper. He sees the future of OLAP systems as columnar stores - and was a founder of Vertica (subsequently sold to HP).

Finally, now the background is out of the way, to address your specific question. He is saying that because many of the NoSQL architectures are disk-based (i.e. they don't run in memory), these much-vaunted systems will in fact suffer from the same disadvantages as OldSQL (which they were meant to replace), and so not only will they not be faster, but they won't be consistent either - a double-whammy loss as far as Stonebraker is concerned. 

Google such terms as "VoltDB architecture", "NewSQL" and "columnar store". That should give you a few leads in this (very interesting) area.