Specifications from the Luftwaffe Resource Center:
Type: Long Range Bomber or Reconnaissance aircraft.
Origin: Junkers Flugzeug und Motorenwerke AG
Models: V1 to V3 and A-1
First Flight: Prototypes only
Final Delivery: None
Number Produced: V1 and V2 Only
Model: BMW 801E
Type: 18-Cylinder two-row radial
Wing span: 165 ft. 1 in. (50.30m)
Length: 112 ft. 2.5 in. (34.20m)
Height: 22 ft. 7 in. (6.89m)
Empty: 81,350 lb. (36,900 kg)
Loaded: 166,448 lb. (75,500 kg)
Clean: 314 mph (505 kph)
Max. Ext. Load: 267 mph (430 kph)
Service Ceiling (Typical): N/A
Range in Recce configuration:
6,027 miles (9700 km)
Endurance in Recce configuration:
Transport (V1): 22,046 lb. (10,000 kg)
Bomber (V3): 3,968 lb. (1800 kg)
Just looking at the specification of the Ju 390 it is an excellent reconnaissance/patrol aircraft. Extremely long legs, and a relatively high top speed. Like many German bomber aircraft/designs the payload is somewhat lacking compared to Allied aircraft, but it has a vastly improved range compared to other German bombers (to give Germany her due, she never really had any heavy bombers only medium bombers like the He 111, as there was no really focus in that area by the German high command).
The Ju 390 did not make into operational service by the end of WWII in Europe. The first prototype aircraft (of which 26 production aircraft were ordered) was completed on 20 October 1943 and took part in tests (including inflight refueling) until March 1944. A second aircraft (Ju 390V2) was completed sometime in 1943 with the first flight taking place in october 1943, with testing continuing until sometime in February 1945.
The Ju 390 has in recent years become the subject of a rumor stating that a Ju 390 flew from France to within 20km of New York City. This is the subject of some debate, as there is some evidence (Ultra intercepts, and POW interrogations) to indicate such a flight did take place. However, what this rumor does not take into account is any radar system covering the approaches to NYC would have spotted it. NYC was then a hub of shipping, manufacturing, and had many major war contractors in the area. While it would be theoretically possible for A Ju 390 to make such a round trip, it would have to be modified to carry ~50% more fuel and would have been unable to carry any meaningful payload. There are also rumors a Ju 390 carried a Japanese general back to Japan via a polar route, and that a Ju 390 made several transport flights to Argentina before the war ended.
The Ju 390 is an interesting aircraft as one of the few really long range aircraft produced at any level by Germany. It's planned use, bombing the U.S., thankfully was never used, but from a purely aeronautical standpoint the Ju 390 was an excellent aircraft.