The BK-7m has a lot of good sounds, AFAK mostly identical to the E-80, about 1,100 tones altogether. Its pianos are really good! Strings and acoustic guitars are not its strength, the acoustic guitars in the styles lack realism. There are some really good saxophones. Nevertheless, the BK-9 offers substantially more (better string sections from SRX 4, supernatural acoustic strumming guitar etc.). How the BK-7m sounds compare to PA-3X, I can't say explicitly.

Regarding the Integra, besides the 256 (!) SuperNatural sounds, which are NOT spectacular in all cases (artificial vibrato etc.) and don't cover any section sounds (except string section), the orchestral sounds I particularly rate best are those from the expansions SRX 04 and 10 (all 12 SRX are included, but only up to 4 can be used at the same time).
The Integra always works in "Studio Set" mode, i.e. you have 16 parts, which you can assign to theoretically up to 16 keyboard zones or 16 midi channels. So in that way it is easy to combine it with an arranger via midi - only there is the restriction that you can only call up 64 different studio sets (=registrations), the Integra has no more storage locations for studio sets. Workarounds for this restriction are iPAD apps, controllers or patch bays which can store different midi sets to address different midi channels with the push of a button, or send midi patch change messages.