So how many men were lost in the battle?

There are some interesting discrepancies here:
Numbers from the PAA KTB, shortly after the battle:

German losses (Officers/Other Ranks - Share of total strength on 18/11/41)
KIA 104/1,032 (7%/7%)
WIA 144/3,339 (8.5%/7%)
MIA 201/9,940 (10.5%/20%) (of these 4,500 Bardia/Halfaya)
Total 449/14,311 (14,760)

Ital. losses (Off/OR - Share total strength on 18/11/41)
KIA 85/951 (3%/1.5%)
WIA 155/1.967 (4%/3%)
MIA 1.172/17.382 (34%/30%) (of these 8,000 Bardia/Halfaya)
Total 1,412/20,300 (21,712)

Axis total: 1,816/35,060 (36,876)

Material (German/Ital.- Share total strength on 18/11/41)
Tanks 220/120 (85%/80%)
Guns 42/181 (40%/48%)
Aircraft 170/105 (160%/150%)

PAA KTB assumes Commonwealth losses as this:

10.000 KIA/WIA
12.000 POW
1.623 armoured vehicles (tanks/AC/carriers)
2.500 motor vehicles
329 Aircraft

The brit. official history which is based on German/Italian records, and of course the Commonwealth unit records, gives the following losses to mid January, without Rommel's counter offensive.

Total strength/KIA/WIA/MIA/Total/Share of strength 18/11/41
German 65,000/1,100/3,400/10,100/14,600/22%
Ital. 54,000/1,200/2,700/19,800/23,700/43%
Axis total 119,000/2,300/6,100/29,900/38,300/32% (13,800 of these MIA
inBardia/Halfaya)

Brit. 118,000/2,900/7,300/7,500/17,700/15%

The counter offensive at end Jan. was no big deal for either side interms of losses, apart from the ca. 1,000 POW of 7th Indian Brigade,which was encircled east of Benghazi, but able to break out, but this must account for most of the discrepancy in the POW numbers of the Commonwealth forces.

Now for the real puzzle: Italian numbers for Italian losses are much higher than either the British or German numbers:

Ital. losses from Italian Official History 15/11/41 to 15/1/42
Officers/NCO/OR/Libyans/Total:
1,945/2,674/34,974/2,674/42,185
Material:
Autom. support weapons: 3.200
Mortars 89x81mm/307x45mm
Tanks 63 medium/187 light (all light tanks lost)
Armoured Cars 25
Anti-Aircraft guns 320
Guns all calibres 584
Motor vehicles 5.000

The Italian official history also gives Axis strength as higher than the British OH:

Germans 70,000
Italians 100,000 (they count everyone including chaps in Libya, is my guess)

As you can see there are significant discrepancies in the numbers, and the KTB of PAA has to be seen as the absolute lowest for the Axis losses. It is likely that the most relevant number is the one from the British official history.

If anyone has further insight, please contact me.