For any 3E group I played in, healing was NEVER the limiting factor that determined when rest time was. The remaining highest-level spells of the caster(s) was what determined rest times. If your encounters don't require the caster(s) to unleash the highest-level spells, then they are too easy - of course you can do many in a day. However, if your encounters are appropriately challenging, it is almost impossible to do more than 2-3 of them in a day - the caster(s) end(s) up dry...
For 4E, it should scale similarly all the way up - you should probably be able to do 6+ encounters in a day at any level.
I disagree. At high level there were many encounters in dungeons that did not take up much of the players resources. There were a few hard fights now and again, but most of the wandering monsters and such the fighters and melees could handle with complete ease without the caster having to cast a single spell. The only groups I've seen unable to continue on were those with groups that had wizard players that felt compelled to release as many spells as they could on every single encounter.
And you get many more spells at high level than 4E characters even taking into account encounters. So I seriously doubt the adventuring day was shorter in 3E than 4E for high level characters. My group and I could finish entire dungeon levels and then some at high level without expending our resource pool. Then again 3E fighters were damage machines unlike 4E fighters.
You must have a group without very good melees if you couldn't handle encounters without your wizards blowing off all their spells. I certainly didn't travel in groups like that. The only time we had knock down, drag out fights was with end game rooms against main villains or their number one henchmen.
It's astounding how much play experience can differ. I know with certainty that 3E characters can go longer than 4E characters if they are smart players with rare exception. 3E had many rooms that characters could steam roll with the rare end game rooms that were a very tough fight. But most rooms or encounters were far from a tough fight and many were designed as lesser encounters to slowly wittle away resources.
So I guess the best answer to the OP is it depends on your group. I know my group could handle very long adventuring days in 3E at about lvl 7 and above. We were highly organized, kept a fund for the purchase of healing wands and magic items, focused on organized tactical fighting, had casters that used magic when it was needed rather than every chance they had, and used scouting to efficiently evaluate tactical threats and remove traps and the like in our path.
When you do all that I stated above, it comes down to resources. Due to the inherent limitations of magic items and healing surges, a 3E character can go longer than a 4E character.