I have upgraded my site from 3.4.8 to 4.0.13.1 succesfully too with only some minor problems . Here are the details ;
During upgrade process I had a table corruption causing "Error : Incorrect key file for table 'ips_core_notifications'; try to repair it " Tried to repair both thorugh cPanel or command line using putty but it did not help. Finally I found out that truncating the table was the solution. After doing this and a Retry, upgrade was succesfully finished in around half an hour
Background processes last almost 16 hours ( I manually ran it ) . That was more than I expected. ( 500.000+ posts might be the cause )
I realised a forum's permission was altered causing new members unable to post their introduction messages.
Gallery pictures were incaccesable cause picture URLs were prefixed by site adress (as http://www.sitename.com/http://www.sitename.com/gallery/image/1844-imag3334/ ) . Support quickly fixed it saying it was a bug of the upgrade process
The "Click and Edit" feature for titles was unusable cause the java script was not put in place during upgrade which was again fixed by support quickly.
Special thanks to IPS Support as the replies and fixes were quite fast.
And another thanks to @Woodsman for this great topic
And a final note. I was not sure how the site would perform after the upgrade in terms of response times and page creation. The site performs quite fast till now ( 2 core, 2 GB memory VPS ) . I have memcached installed but not applied it to IPS4 yet cause had some errors on test installation and have read there are some problems with memcached-4.0.13.1 which will be fixed in 4.1
Anyone having 4.0.13.1+memcahced configuration without any problem ?