To make an electronic organ sound like a conventional pipe organ, the most important component is the sound reproduction itself. Even on your tiny one-manual ten-stop instrument, a full 8-note chord can sound 80 pipes simultaneously. On a larger instrument, there may be several hundred individual pipes sounding together.
In contrast to this, an electronic instrument only has a very small number of loudspeakers. That has two consequences.
The first is that there are only a small number of physical locations where the sound is produced. In a pipe organ, very pipe is at a different location, and the sound creates a slightly different reverberation pattern both within the instrument itself (e.g. the location of the different pipes in a swell box) and within the whole building. The complete ears-and brain system of human hearing has remarkably accurate direction-finding capabilities, and though the difference in position of every pipe isn't consciously heard, it is certainly affecting the overall hearing process. Because of the effects of the building acoustics, often a single sustained note on an organ can sound quite different if the listener moves only a few inches. Since humans subconsciously make continuous small head movements as part of the direction-locating function of hearing, these effects are significant.
On the other hand, an inexpensive electronic instrument will have a small number of loudspeaker cabinets, each reproducing the sound of many (or all) the pipes, and this detailed spatial differentiation is lost.
The second problem with a small number of loudspeakers is the distortion produced when one speaker reproduces two simultaneous notes. It is impossible to devise a reproduction system that is completely linear, and therefore when a single loudspeaker reproduces pure tones with frequencies f1 and f2, it inevitably also produces frequencies like f1-f2 and f1+f2 which were not present in the original.
This "intermodulation distortion" doesn't show up in demos which reproduce single tones, because in that situation it doesn't exist. Even reproducing a the complex tone of a single organ pipe (e.g. a solo reed stop) the issue doesn't have much effect, since all the distorted "intermodulation tones" are actually at the same frequencies as the harmonics of the undistorted tone. But for the very complex tonal structure of real organ music, the cumulative effect of these small unintended sounds is to "blur" or "deaden" the overall effect.
So the bottom line of all this is not to buy the instrument with the biggest selection of nice-sounding stops you can find in your price range, but the instrument with the most sophisticated loudspeaker system you can afford. You might consider that the "advanced" edition of Hauptwerk, which is one of the "standard" software packages for playing pipe organ samples, can produce up to 512 independent channels of audio output. It's unlikely that you need as many independent amplifiers and speakers as that (you would be getting close to the "ideal" situation of one loudspeaker replacing each pipe of your current organ!) but as rule of thumb, more audio channels is better. High quality digital organs in large buildings will often have 40 or 50 independent audio amplifier and speaker channels, not four or five.
There is another consideration here: the "best" design of the physical layout of your audio system is critically dependent on the layout and acoustics of your building. If your proposed organ supplier isn't going to visit your building, measure its acoustic properties, and then recommend one of their standard designs - or better, produce a customized design - consider buying from someone else!