"Over-year" hay is better for horses; in fact some say that you should never feed this year's hay to horses.
We've fed 2, 3 and 4-year old hay to sheep with no problems, and it has always been the case around here that in a good year you make as much hay as you can, and can store or sell; you may make less or none next year so it's always good to have enough over to give you a good start.
I would estimate that about 1/4 of our winter feeding this year, of cattle and sheep, will be 2011 hay. There may well be insufficient hay for the ponies (natives), so the Fells could be getting up to 2/3 straw, the Dales' 1/3. We'll be mixing straw with this year's 'orrible wet silage, for the cattle, too.
In terms of which is better, it depends on when it was made, how, what leaf, etc, and what it is for. For feed value, I'd rather feed 2011 July hay (we had a real good spell at the end of July last year) than 2012 August hay.
Cattle need better hay than sheep, for native ponies very poor hay is plenty good enough. (For ponies, I want proper meadow grass - lots of timothy, etc - and not monoculture rye grass.)