In theory, should be slightly faster.
However, just picking a random schedule, 2109 from King's Cross, here is the timings from King's Cross to the first station stop at Letchworth
365 2109 to 2136 with 1H performance allowance (27 minutes)
387 2109 to 2135H with 1 performance allowance (26H minutes)
However, if we take the performance allowance out, it becomes
365 - 25H
387 - 25H
I'll have a more thorough look tomorrow when I have more time!
As regards performance more generally, departing King's Cross there wasn't much difference between a 365 and 387 until about Alexandra Palace. From there a 387 would reach 100 mph by New Southgate, whereas a 365 would take until Oakleigh Park or New Barnet depending on how the neutral section at Wood Green Feeder Station was handled by the driver. If the 365s were allowed to coast for longer this could add quite a bit extra to when 100 mph was reached. 387s took longer to power up again after the neutral section, but would regain the lost speed quicker.
Watching 365 performance was always interesting as compared to 387 or 700 it felt they were working that little bit harder. 317/321 were even more interesting, as they *really* had to work hard on this section, and with much more variability between different units - an average 317 pair would reach 100 by about Hatfield, whereas a bad pair might not achieve it at all.