Choosing between MyISAM & InnoDB - two servers with related tables
"MyISAM is faster than InnoDB" -- This is an old wives tale.  It used to be somewhat correct; now it is somewhat incorrect.

SELECTing during UPDATEing -- MyISAM is usually fast enough so this is not an issue, but InnoDB will usually not block at all.  Go with InnoDB.

Power failure -- InnoDB automatically recovers.

You are talking about two "servers" -- Do you mean two different computers?  And two differen instances of mysqld?  There is nothing to have them talk to each other.  (OK there are Replication and Federation, but it did not sound like you are into those.)

If you really meant "database" or "table" on a single MySQL instance, then so state.  Tables (even in different databases) can be JOINed for most operations.