An anaconda, with shields, can get 39 LY with a full tank of gas. An asp, with shields, gets 34 LY with a full tank of gas. That extra 5 LY means you can take a more direct, more linear route to wherever you're going, and you'll need to do fewer jumps to cover every 1000 LY you travel. An anaconda probably shaves 2-3 hours off of any trip to the galactic core, and there are some systems/regions, particularly in the outer rim, that are simply inaccessible by asp.
Also, the anaconda can fully refuel at a star faster than an asp owing to the larger fuel scoops you can fit. You do a lot of refueling while exploring - so something to consider. The anaconda runs colder than an asp, so if you fly to close to a neutron star, you'll end up taking less heat damage.
That being said, there are arguments in favor of the asp: it's much cheaper, and it turns much faster.
Imo, if you have the money and don't have to sell any of the other ships you use to pay for it, go for the anaconda. Otherwise, the asp will probably get the job done just fine. I've done 20k ly trips in both and I prefer the conda because it gets you where you want to go faster.