Are InnoDB tables harder to backup and slower?
Have a look at this link What are the main differences between InnoDB and MyISAM.?

After looking into this you will somewhat able to decide what to do.

From your question prospective :

1.InnoDB is slower at most things:

It is not true well designed InnoDB tables performs very well i have a 1TB of data with InnoDB table and is performing well

the reason for poor performance may be


  improper use of indexes 
  
  fragmentation in tables  
  
  improper setting of innodb variables like innodb_buffer_pool , log
  files,how the table space is configured


There may be a lot of reasons due which it doesn't perform well. Have a look how to tune InnoDB Performance

2.InnoDB is hard to backup

It is not also very hard to backup the InnoDB tables there might be time that you feel it is tough because of its table space/log files/frm files.As for a large MyISAM table you can directly copy the databases using the copy operation and it is quite fast.

due to that you might feel that backing up InnoDB is hard but it is not so.

There are proper backup techniques for InnoDB tables also, please see the following link for this Backing Up and Recovering an InnoDB Database.

3.InnoDB only shines when you have complex joins on tables with udpates and inserts.

No they can also perform well in all cases in which the MyISAM can.