Being a southern hemisphere person my first reaction was a comparison with the Large Magellanic Cloud.
It is quite distinct and looks like a piece of detached milky way. Under dark sky conditions you can just see the Tarantula nebula .... which means it is intrinsically vastly brighter than Orion. They go very high in the sky from Tasmania.
Also from the southern hemisphere the galactic center and bulge goes overhead. In very dark sites you can see faint shadows.
A better comparison in the Andromeda galaxy. The Milky Way is a bit dimmer. So as a first estimate the Milky Way would look like Andromeda from a distance of 2 million light years ie on a dark night a easily noticeable fuzz brighter in the middle about 1 deg across.
Estimating what the Milky Way would look like from say the LMC or closer 50,000 (dragon04) light years is trickier.
The key is the surface brightness. Take Andromeda, if you half the distance the total brightness will go up by a factor of 4 (inverse square law) but the area will also go up by a factor of 4 (each side of square will appear twice as long) so the overall surface brightness stays constant. Cavet: this is based on small angle approximation and could break down, but will hold for each part of the galaxy we look at. So I will continue along these lines.
So the surface brightness stays the same. So the contrast between the Milky Way and the sky of our hypothetical planet will be about the same as for here on Earth. The Milky Way will look about as bright but bigger, and point like objects clusters, nebulae, stars will look brighter on the background.
Now most of the Milky way we see in the sky is disk, the brightest surface brightness (most stars in an area) is toward the bulge. Away from the dust lane there is about 1 to 2 magnitudes of extinction (absorption) caused by dust. So the outer bulge would look 2-4 times brighter. The center of the bulge is blocked from view, but taking the bulges as a giant globular cluster the central region would be another 2 magnitudes brighter (roughly from how I remember globular clusters: a lower limit estimate can be made by considering slices through a uniform ball of stars about 2 times brighter (1 magnitude), but stars are much more packed at the center in globulars, and the bulge). So we have 4 magnitudes, lets be generous and give it 5 (= nice 100 x factor) magnitudes brighter when view unobscured.
So from the LMC you would have a tilted disk about 35 deg across (trig here: half size galaxy 50,000 ly, distance 160,000 ly , half angle=ArcTan (50/160) =17 deg) with a bulge about 3-4 deg across starting twice as bright as the Milky Way (as seen from Earth) and getting brighter in the middle. (Bulge about 10,000 ly across). The bulge would look like the head of a large bright-ish comet, Hyakutake maybe). Depending on tilt the disk surface brightness would be comparable to what the Milky way looks like or the LMC. You would be just able to spot the few very brightest stars and nebulae.
Now from only 50,000 light years the disk of the galaxy would look be about 90 deg from edge to edge (easy triangle 50,000 ly distance, half size 50,000 so 45 deg triangle). Unfortunately from above the surface brightness of this disk would be much lower than how we see the Milky Way because you would be looking through the thin disk rather than along the disk. It would be like looking away from the Milky Way in our skies without the stars. Everything except the bulge would be further away than 50,000 ly. Only a few super massive, super bight stars would be visible, with a few extreme nebulae and clusters. Recall M13 globular is only 25,000 ly and is just visible. Now the bulge could look much more interesting. It would be 11-12 deg across and look maybe 40 -- 100 times brighter than any patch in the Milky Way: like a big bright comet head (say a large version of Hale-Bopp).
Maybe the best view is just above the plane near the edge of the galaxy.
After doing this thought experiment I am a bit disappointed.
Nothing like the Cosmos galaxy rise.
Now for s spectacular sky, live in/near the bulge or in a globular cluster. A sky covered with hundreds of stars the brightness of Venus on a nearly uniform glow of stars.