What would be a good way to test data in different projections have identical locations?

I have 2 sets of files for which I want to compare the coordinates of ~3000 plots

1. I have a 38 shapefiles of surveyed plots in different regions of Northern Canada. Some of them are projected in Lambert Conformal Conic, others are projected in Albers Equal Area.
2. I have an Excel database with these same plots. However, in this database, the plots are provided in UTM. They cover 13 different UTM zones

I want to know if the locations of the plots are the same or different between the shapefiles and the Excel file. I'm expecting to find instances of both, and I want to know for which plots the coordinates have changed.

My solution to try to figure this out was to use R to measure the distance between each plot's location in the shapefiles and the Excel file. If the result is 0 , the location is correct. If the result is >0m, I need to identify which location is correct, and change the one that is incorrect. Realistically, I could probably count them as equivalent if they're less than 10-15m off.

I had individually converted the UTMs from each zone to Albers Equal Area, and then all of the shapefiles to Albers Equal Area. However, someone mentioned to be that Albers Equal Area is good for measuring area, but not distance.

I thought I would re-run my code, but convert everything to Lambert Conformal Conic instead. However, read a source saying: "Conformal projections preserve the correct angles between directions within small areas, though distorting distances."

I'm stumped. What WOULD be a good projection for measuring distances?

Or alternatively, is there a better way to approach the problem of testing if data in different projections have identical locations?

(I would prefer to use R. Usually I have access to ArcGIS, but I don't right now due to the pandemic. I have downloaded QGIS but I'm not very comfortable with it)

• Perfection is reprojection is rare. Does it matter if the location distances vary by 1mm? 10cm? 10m? The difference will play into projection suitability. If the raw data is telephone GPS, 30 meters might be close enough. – Vince Apr 29 '20 at 16:52
• Thanks for the clarification question, I've edited the question accordingly. I think I'd like to know if they're more than 10-15 m different from each other – canderson156 Apr 29 '20 at 17:51
• Either Lambert or Albers should be fine for 10m distance. If they're off they should be really off, so computing distances with what you have should probably step one. – Vince Apr 29 '20 at 18:03