First, thanks for printing clear photos.
Second, may we assume that you are using PLA? If PETG, then have you dried it?
Third, may we assume that the extruder and hotend are the same and that the P1 extruder was upgraded?
I’m assuming that you are dissatisfied with this section of the left hand print circled in red where there appear to be voids. I also see some stair-stepping, circled in blue. Is that what you mean by overhang? I ask because I’m not seeing any overhangs so if it is possible to draw an arrow to what you don’t like, it will easier to answer the question. Perhaps if you could do a closeup pic or a macro pic, that too will help.
In any event, if I were to take a first stab at it, it looks to me that these were printed at two different filament heights.
If you haven’t already done so, one way to rule out different settings(such as layer height) as an issue, is to save the .3MF file directly to the SD card and print it from the menu. Alternatively, you could FTP it directly. Now I realize that if you take a .3MF that was meant for a P1, you might find the P1 definitions stuck when you send it to the X1 but humor me and try it anyway and slice it even if the settings complain about incompatibilities. I’d recommend using P1 settings in the X1 since the P1 features are a subset of the X1. That said, I’ve not tried so perhaps another member with two printers can speak better of this. If you are able to reproduce the same differences seen in your photos but have then ruled out settings, then I would chase a hardware problem like perhaps your extruder needs to be upgraded on the P1.
The other question is; have you calibrated the filament on both machines and saved them to different filament profiles? One could be suffixed with -X1 and the other -P1.
One of my favorite troubleshooting techniques, which, while doubling print time, is to use the quiet mode at 50% speed. If there are filament calibration issues or stiction issues with the filament feed, 50% speed will ameliorate a lot of sins in the filament calibration or extruder issues that might be at the hairy edge of tolerance. Either way, it is the easiest one-click experiment one can use to troubleshoot a pesky issue.