If you're running V brakes, get horizontal drops or fork ends.
If you're running disc brakes, and you're the set-and-forget type that rarely changes gearing and you hardly ever get flats --or if you happen to be a serious weight weenie -- then get horizontals. Removing and inserting the rear wheel can be a bit of a pain, but if you rarely have to do it then it's not a big deal. Some combinations of frame+caliper+rotor+axle position will allow you to just slide the wheel past the caliper. Some combinations will still let the axle through if you line the notch in the rotor up with the edge of the caliper. And some will require you to loosen the caliper bolts, thus having to reposition it after the wheel goes back in: in my extensive Surly experience, when you're doing this in the field, the caliper never ends up in quite exactly the same position -- and/or the wheel never ends up aligned quite exactly the way it was before -- forcing you to fuss around with adjustments further or put up with rotor rub for the rest of the ride. When you're in the comfort of your own shop this is not a big deal, but I've had to do this in the field numerous times, including twice along the side of a road, at night, in cold pouring rain. Afterwards I was more Surly than my Karate Monkey. My stance has softened a bit since I've learned the rotor-notch trick (coupled with some careful dropout filing), but all else being equal I'd rather this bike had an EBB on it.
If none of the above applies to you, go with sliding vertical dropouts or EBB. Biggest downside of either method is weight: most eccentrics weigh a couple hundred grams (though they can be machined lighter) and sliding vertical dropouts aren't much lighter than EBBs. I lean a bit towards EBB myself, since sliders require you to tighten 4 bolts and observe proper wheel alignment within the rear triangle, although it's probably not that big of a deal. In any event, my set-screw EBB has been 100% trouble free and has never creaked or needed any maintenance whatsoever. I don't find the change in saddle position relative to the BB to be a big deal, since the range of adjustment is only about 1/2" horizontally or vertically, and a change in either plane can easily be corrected with a quick seatpost adjustment. Chain growth is mostly a non-issue: with good chainline and cogs, my drivetrain is pretty forgiving. I adjust the EBB once each time I put on a new chain, once again when the chain has broken in after 50-100 miles, and that's it.