Ts870S has one of the best sounding receivers on RX. There are very good reasons why it sounds so good.
The only problem is the TS870S poor transmitter which has horrible TX IMD performance. If you using it to drive a amplifier at 50 watts or less its just barely OK. If you use it on ESSB you will cause a lot of interference. The ALC
on TX is one of the worst ALC's designs it causes so much splatter.
The TS940S is good receiver and a transmitter with exceptional IMD performance when compared to the current crop of top notch radios. It puts radios like the K3 and IC7700 to shame in the area of transmitter cleanliness.
If you a big gun driving a big amp I would take the TS940S over the TS870S any day.
I would not worry about receiver performance, non of them overload or have problems. You should be more concerned how they work on transmit. I still have a TS930S, TS940S and TS830S. Let me tell you have I have compared these old work horses to just about every modern top dollar radio. You missing nothing buying a good radio like the TS940S period. Dont become obsessed by the silly receiver numbers games. It means very little to the average ham who has average antennas and suburban noise.
What matters is having a good sounding receiver, a clean transmitter and having a noise blanker or noise reduction system that works for your QTH. Good ergonomics are also very important. No point having a radio like the K3 that has a excellent receiver that you only need 1% of the time and then have poor ergonomics and a lousy lack of knobs that gives you heat burn every time you use it. Contesters brag how good the receivers are of these super duper duper radios, yet they only get on the air in contest season(most of them) Their 6 200 ft towers with stacks idle, while the average ham is on the air every week fighting plasma TV and other QRM enjoying the hobby. Good receiver numbers dont matter when you have a S6 noise floor.
Have had the 940 now for a few years, it has served me very well and still does.
Been looking at an 870, like the DSP options it has. Not sure which way to go. Keep the 940 or get the 870.
What are your experiences with the 870?. These were build from 95 to '04 I believe. Any particular serial number range to stay away from?