Exploration OTOH is very vague. The overall structure is described by nothing more than the play loop, which is the most general rule in all of 5e. Sure, there are potentially many resources that can be applied, and subsystems invoked, but it is CERTAINLY the least well-defined sort of play in 5e, and doesn't even specifically invoke the idea of a scene, or any sort of resolution at all (it is not only standard for the GM to handle this entirely on his side, it is COMMON for that to happen). Contrast this with the exploration rules of 1e, which specifically break time down into turns, describe the types of decisions the party is likely to need to make, provides specific rules for resource usage, etc.
This is kind of an interesting subtopic as I think exploration (particularly wilderness exploration) is a challenging aspect of play, especially when people are first starting. I find that no matter what tools and procedures a book lays out, people tend to do what they think works best. AD&D has some very good options, but those options can also be constraining if your players have difficulty fitting easily into that turn based structure (works great if your players take well to it). With D&D specifically, I like having a variety of tools and procedures that I can draw from. Sometimes, I find thinking in terms of AD&D turns very useful, but there are places in play where that might break down and things need to open up.
How I handle survival in my own games is there is a Survival Skill. It is grouped into subskills for different environments, like Cities, Mountains, Forests, etc (obviously there is sometimes cross over and you just have to pick one that fits best). You roll Survival to successfully navigate but also to successfully navigate around any encounters or challenges. And the 'turns' scale depending on the environment and situation. So traveling one 30 mile hex on the map might be a single roll for a day of travel. But in a city I might ask for the players to roll whenever they move between wards or city quarters. And if they are inside a persons house or slipping into the king's castle, they may have to roll survival every ten minutes (like a turn in an AD&D dungeon crawl) or they may have to roll in each room or every couple of rooms depending on how the place is set up. I find a sliding scale of granularity works best for me in terms of time. Generally the more zoomed in the location the tighter the timing on the rolls. Also some places might require multiple rolls due to challenges inherent to them.
All that said, I also quite liked the approach that the 5E Middle Earth took to overland travel and exploration (a very different approach). I also am fine in a group where things are much more open and the GM is just kind of responding to what the players do.
When it comes to exploration, as a player I am pretty much open to different methods. The only time I get annoyed is if it starts to feel like we are playing a complex computer game or a board game. I still want to feel like I am there, in the action, not like I am a piece on the board.