This is my question too. I'm trying to adapt to the new Photo format and appreciate how it's consistent across all devices, but I really liked how iPhoto organized according to events.
I understand that I can still create events, but it seems that when I create one it still leaves the photos in the stream, and that if I delete a photo from the stream it deletes it from the event I created on my laptop.
iPhoto had Albums, Photos and Events. (And Shared Photo Streams)
Photos has Albums and Photos. (And Shared Albums)
For many people Events in iPhoto were really confusing - photos could only exist in one Event and not many really understood how to move photos between events or that when deleting a photo from an event you were really deleting it "for good". Myself, I liked Events but doing them "right" did mean a certain amount of micromanagement. But I enjoyed that.
Photos in iPhoto were just one big listing of all your photos (with event titles optionally shown, which from what I've seen observing friends and family) just confused most people.
iPhoto also has Albums which are actually virtually identical to Albums in Photos. In iPhoto you can put photos into as many albums as you like. They are "references" so deleting from an album doesn't really delete the photo. (In Photos.app you right click and "Remove from Album" - not delete)
Shared Photo Streams in iPhoto are something "special", and kinda act like Albums shared with others.
Photos.app is similar but different. It's really much better when you understand the differences and how the model is simpler but better really.
"Photos" is all your photos arranged automatically for you. It's arranged by "Years", "Collections" (Photos taken around the same time in about the same place) and "Moments". My 34,000 photos are fully geotagged and have correct dates this this "Photos" view provides a reasonably decent overview of my library. For something done automatically this is going to be really awesome for the vast majority of people that have no desire to micromanage their photo library. It's the "it just works" view that mostly works really well.
Albums are where you get to micromanage. iPhoto Events transfer over as Albums. Shared Photo Streams are just Shared Albums. You can create as many albums as you want. You can create folders for albums and folders of folders (say a folder for different clients or different years). Putting a selection of photos into an album or new album is easily done via the New Album menu item (which is a bit poorly named, as you can add to existing albums or create a new album for the selected photos)
Photos can exist in multiple albums (though there's no way to see what albums a photo belongs to - say like in iTunes where you can see what playlists a song belongs to -- i've submitted a feature enhancement request for this, I suggest others do the same). Editing a photo that exists in multiple albums shows those changes in all albums (obv since albums are just "collections" of references to photos)
Deleting photos from an album doesn't delete the photo from your library. In all cases the only way to delete is to right click and "Show in Moment" and then delete there - that's a "real" delete from your library. (This differs from iPhoto where you could "delete" from either Photos or Events and that was super confusing to some people - I've heard more than once... "I didn't mean to really delete it for good I just didn't want it in that event")
There are some special albums: Faces, Panoramas, Videos are all special "built-in" Albums. Favorites is considered an Album. Smart Albums work exactly as you would expect. There's also a special "All Photos" album which is essentially the old "Camera Roll". It's just a raw dump of all your photos in the order they were taken/imported/etc. I actually never use this and would be just as comfortable if i could hide it.
The one difference between the apps that changes is where iPhoto automatically created Events for you (and sometimes you needed to tweak them to get pictures where you wanted), in Photos.app you need to create Albums on your own after importing pictures (or taking a batch of pictures, etc.)
But honestly, if you were the type that micromanaged your events and kept them "clean and organized" in iPhoto, that won't change in Photos, you'll just do so using Albums.
It's different, but really the same and, in my opinion, better.
It's going to be much less confusing for most people.
I preferred the old way, where I could download from the stream to my laptop, then delete the photos in the stream to free up space. If I wanted to share across all my devices, I could make shared folders in my stream. Are these features gone forever with Photos?
Photo streams as you know them are gone. You just get all your photos. Period. No special album or anything. Take photo on your iPhone, it's just there in your photo library on all other devices. It's very sane and sensible to the average person.
If you don't want a photo, delete it and it'll be gone from everywhere. If you want to share it to "Shared Album" (i.e an old Shared Photo Stream) just do it. It doesn't change that you have one copy of the photo in your library appearing in an album (at least one, but could be more) which just happens to be a shared album to other people. (I can check but pretty sure that sharing a photo to multiple albums doesn't change space, and I think if you edit the original photo that edit it pushed out to everyone, but i'll have to check that.)
It really makes a ton of sense in practice. Again this is much easier for most people to "grok".