You rang?

Unfortunately I haven't tried the one built into the amp head, so I have no idea how it compares.
Re: the trim pots inside, they make a pretty big difference in the performance of the multiband mode, so I would recommend doing some more experimenting and careful listening, while in that mode. It does sound like the multiband mode is really what you need; the tubesim mode is nice, but it won't serve the main goals you described.
Also, be sure to adjust the level of your signal going into the pedal, as that can make a dramatic difference in how it responds to you.
Beyond that, if you can swing the $$$ I recommend you try a FEA Dual Band comp pedal, or for a bit less money try a used Rane DC24. Either one of those will allow more "sizzle on top" than the EBS.