Sorry for the slow reply. I have limited experience with the 500-series models, and wanted to make sure I had my facts straight before responding.
There are two internal GPS models in the 500 series, 597ci and 587ci. Both feature 4.5″ diagonal screens. The 597ci has twice as many pixels in that area than the 587ci does (597ci: 640 x 480; 587ci: 320 x 240), so your resolution while using the chartplotter of the sonar function will be better with the 597ci.
Both the 597 and 587 have 50-channel GPS receivers, just as you’ll find in the other Humminbird fishing systems. One distinction between these models and the 700-series units (and up) is that the 597 and 587 are only compatible with Navionics Gold or Hotmaps (not Lakemaster).
By moving up to a 788, you’re getting a larger screen (5″, 640 x 640 pixels), Lakemaster compatibility, and compatibility with all of HB’s accessories (weather sense, XM weather, Interlink, etc).
If you pay close enough attention, you should be able to score a deal on a used 788. I just sold one that was on the bow of my boat for a couple months (which is getting replaced by a new 898). My recommendation would be to move up to a 788 and experience all of the power and possibilities of a true Humminbird fishing system, rather than being limited to something that is just a graph.