If you are using a fleet carrier as your "base" for exploration, then it doesn't really matter what ship you use for exploring. I have seen some streamers use the Eagle, which according to them is a superb exploration/exobiology ship for short distances.
Nowadays I wouldn't be surprised if they prefer the Cobra Mk V instead, because of its superb SCO handling. (Also its jump range is actually really decent.)
However, if you are not using a fleet carrier, then the range of options becomes much more limited, particularly if you want to travel very long distances (thousands of Ly).
Before the new SCO ships, the four classic were, of course:
- Asp Explorer: The "old reliable". Ugly, sounds like a badly tuned diesel engine, but decent jump range and internal slots. Excellent canopy view.
- Krait Phantom: Very stylish and "badass" looking, slightly larger jump range than the AspX. Turns slower. Decent but not great canopy view.
- Diamondback Explorer: Second-best jump range (before the Mandalay), rugged look, excellent canopy view, small footprint (thus can land on a postage stamp). Suffers from supporting only a class-4 fuel scoop.
- Anaconda: By far the largest jump range (which was actually a mistake that they never "fixed"). Good to set world records, but it's a huge ship that turns like in molasses and requires an airport to land. It's supposed to be a large combat ship, not an exploration vessel.
Some commanders also liked some other ships. The fifth-most-liked being probably the Dolphin. Very stylish, but it's a luxury passenger ship, not a rugged exploration ship.
Of course now the Mandalay has probably taken the number 1 spot: Very stylish, second-largest jump range by a very small margin, turns like a dream, SCO-optimized, small footprint (allowing it to land even on rougher terrain). A bit poorer canopy view, though, which is its only drawback.
The Cobra Mk V also shouldn't be scoffed at as an exploration vessel: It can achieve quite decent jump ranges (about 70 Ly, even more if you compromise), small footprint, excellent canopy view, and has the best handling of all ships.