So this is about a SELECT COUNT(*) FROM tblname without a WHERE clause. MyISAM has an optimisation for that since it maintains a rowcount for each table. InnoDB and PBXT can’t do that (at least not easily) because of their multi-versioned nature… different transactions may see a different number of rows for the table table!
So, it’s kinda known but nevertheless often ignored that this operation on InnoDB is costly in terms of time; what InnoDB has to do to figure out the exact number of rows is scan the primary key and just tally. Of course it’s faster if it doesn’t have to read a lot of the blocks from disk (i.e. smaller dataset or a large enough buffer pool).
I was curious about PBXT’s performance on this, and behold it appears to be quite a bit faster! For a table with 50 million rows, PBXT took about 20 minutes whereas the same table in InnoDB took 30 minutes. Interesting!
From those numbers [addendum: yes I do realise there's something else wrong on that server to take that long, but it'd be slow regardless] you can tell that doing the query at all is not an efficient thing to do, and definitely not something a frontend web page should be doing. Usually you just need a ballpark figure so running the query in a cron job and putting the value into memcached (or just an include file) will work well in such cases.
If you do use a WHERE clause, all engines (including MyISAM) are in the same boat… they might be able to use an index to filter on the conditions – but the bigger the table, the more work it is for the engine. PBXT being faster than InnoDB for this task makes it potentially interesting for reporting purposes as well, where otherwise you might consider using MyISAM – we generally recommend using a separate reporting slave with particular settings anyway (fewer connections but larger session-specific buffers), but it’s good to have extra choices for the task.
(In case you didn’t know, it’s ok for a slave to use a different engine from a master – so you can really make use of that ability for specialised tasks such as reporting.)