Limits to appearance of a phantom steed

In a recent game session, a player wanted to become invisible and then use a phantom steed to quickly and stealthfully pass through the enemy camps surrounding a besieged city. This began a discussion of whether the phantom steed summoned could be transparent, or nearly so. The spell says:

A Large quasi-real, horselike creature appears on the ground in an unoccupied space of your choice within range. You decide the creature’s appearance…The creature uses the statistics for a riding horse

So what are the limits to the appearance of the steed? While "quasi-real", can it be made to appear so real that an observer would believe it to be a real horse? Can it be made to appear so unreal as to be seen through and receive a bonus on Stealth?

For the limit on how transparent it can be I thought the important restriction is that it has the stat block of a riding horse. Any permanent bonus to Stealth would be included within this block, and a riding horse does not have one. Thus, for me the mechanical limit to transparency would be that it could get a DM-assigned circumstantial bonus (advantage to Stealth checks depending on situation) but not a permanent bonus irrespective of circumstances (modification of stat block).

For the limit on how real it can appear, I looked to the spell Major Image, as an Illusion spell of equal level, whose illusions have the following property

A creature that uses its action to examine the image can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC.

Thus if the steed was summoned to appear real, it would fool any observer who was not explicitly trying to determine its nature, and even some of those depending on the roll. This approach of comparing the spell to same-school spells of equal level comes to me from 1e, with which I have more experience, and in which spells are much less clearly defined in terms of their limits. 5e, on the other hand, has the general principle that "spells do what they say they do". Is such a comparison to another spell then valid?

1. What are the limits to the appearance of a phantom steed? How real or unreal can it appear?

2. When deciding (1), is it useful to compare the spell to Major Image?