They keep updating the apps and website so the functionality changes, but certainly until recently the apps were 'live' streaming, but the web player could be wound back up to 3 hours. I am not on my laptop now, but will check that later to see if it is still possible.
Eurosport often keep a 'video library' of coverage of many events for a week or two, so it is possible to watch those recordings as and when it suits you. Annoyingly though, they have sometimes missed out recordings of some stage race stages!
I would take out a month's subscription and see what you think. If you like it, then save money by getting an annual 'pass'.