Hokay, read the rules more thoroughly. I like the exploration rules in old D&D better, so far. They're not actually very similar.
This system is not a totally modular minigame: it interacts heavily with what you're doing with XP and whether you're exploring or just travelling (i.e. are you using these as exploration rules, or journey rules? Different types of adventures).
In early D&D, you typically want to move as quickly as possible (you don't choose your pace directly, but via the encumbrance load you choose to carry). Moving quickly means triggering fewer wandering monster checks, which is desirable because most XP comes from treasure rather than combat, and in fact in 1e not only do you have the same chance to be surprised at a slow pace, but if you do get surprised it lasts longer (slower movement=moving more clumsily).
In DDN, it's the opposite: by default there's no reason not to move as slowly as possible. Fights are the primary source of XP, so moving slowly allows you to wring more XP out of the adventure, and the fights are easier because you're less likely to be surprised (slower movement=moving more cautiously). There would need to be narratively generated time pressure to encourage a faster pace.
Basically, the choice of pace is not going to be interesting the vast majority of the time. If you're wandering around sandbox-like and using primarily monster XP, you might as well move at the slowest pace. If you're not using XP or using session XP, the choice of pace becomes kind of confused--the rules present slow movement as the smart, cautious thing to do, but it's probably better to book it and accept an increased chance of being surprised in exchange for fewer checks. At worst it's a wash. If you're using quest or narrative XP, or have a narrative reason to move fast that overrides XP concerns, then you definitely should move as fast as possible.
If you're using classic-style treasure XP, it depends how useful searching and mapmaking are. If the dungeon is old-school in its design and you're actually liable to get lost without a map or to miss something important without the automatic search checks, then maybe you'll want to slow down to moderate or cautious. Outside, it will be obvious to either move as fast as possible, or the second fastest speed to make navigation checks if you're off-road.
Also I have to agree with [MENTION=6690511]GX.Sigma[/MENTION]'s first impression--this seems like a lot of checks to make every turn. Playtesting would be required to bear it out but it certainly seems like this would play substantially slower than 1e, and certainly Basic on a turn-by-turn basis. Maybe players will favor a faster pace simply out of real-world tedium.
All in all, I'm pretty sure I prefer the old rules where pace is normally determined by encumbrance load, and faster movement is clearly preferable--then the choice is between how quickly to get through the danger zone and how much treasure to carry with you. Less messy and a more interesting choice (assuming you enforce encumbrance).
I'm not sure exactly how stealth interfaces with surprise during exploration. That part is confusing. But that's confusing in most D&D editions. I'm glad I worked it out for my edition of choice.
