Just off what I can pull from their sites, I'm not sure I'd agree the Xeo takes it, though it's surely different in certain ways. What's most important to you in your computer, and what do you plan to do with it? If you can, play with and dive both of em after reading their respective manuals. It's not that hard to do if you ask around, and it's the best way to know for sure.
Price: Petrel $950; Xeo $999, or $1159 for a kit that has a screen shield (installed on Petrel), a PC interface (Petrel includes bluetooth interface and dongle for non-bluetooth PCs),
Screen: Petrel is LCD; Xeo is OLED... at an earlier time, that would make the Xeo better. Having owned and dove a Petrel, Cobalt, and Predator, though, my opinion is that the Petrel's screen is the clearest of the three even though the other two are some of the best OLEDs on the market. YMMV.
CCR mode: Petrel included, Xeo used to cost extra now seems to be included for free (so sorry, those who bought before)
Battery: Petrel eats any AA battery, Xeo seems to require something special
Interface: Petrel has two sensors that don't pierce the case; Xeo...either you love the tap thing Liquivision does, or it makes you want to "tap" its designer to death for coming up with a solution to a problem that doesn't exist
Algos: Petrel has gradient factors standard, VPM/VPM-B/VPM-B-GF for $75; Xeo has gradient factors standard, RGBM for $149.95.
Interestingly, the Petrel keeps the conservatism of all these editable during a dive, allowing for a customized emergency ascent profile, while the Xeo only offers an emergency "All GFs OFF" setting while diving, causing the unit to go to 100/100 and get you out of the water ASAP.
Screen size: Petrel is 2.4", unclear what the Xeo is
Unit size: Petrel is 3.25"x2.875"x1.375" and sits flush on the arm with integrated bungiee adaptor slots milled into the case; Xeo is 2.5"x2.2"x1.5" and I can't quite tell how it will sit on the arm with it's strap mounts and angled screen
Gasses: Petrel has 5 pre-set OC and 5 pre-set CC gasses, any and all of which can be easily edited while diving to account for a lost gas/using unplanned gas situation; Xeo has 10 pre-set gasses, and this disclaimer in the manual:
Finally, there is an option called "Custom Gas", with which you can configure an additional gas underwater. Doing this while diving is very troublesome, so we highly recommend that you take steps BEFORE the dive to avoid using this option. The best thing is to input every gas you and your buddies are taking underwater. If your buddies use different gases than you do, then you should enter them as "Backup" gases and revert to them in case of an emergency.
Dive logs: Petrel is 1000 hours at 1 sec sample rate, Xeo is 60 hours at 1 sec sample rate, 3600 hours at 60 sec sample rate
Info displayed: Petrel allows one to customize where on the screen info is displayed, as does Xeo and perhaps to a greater extent. However, I think (and I could be wrong, as I didn't read all 78 pages of 'tap 3 times up, then tap 5 times down, left right A B A B up down start select...' Xeo manual) Petrel allows for the display of potentially useful info that Xeo doesn't. These include current GF% (handy for emergency ascents and generally understanding deco efficiency/DCS risk at a given depth) and @+5 (how long will your ascent be if you stay at the present depth on the present gas for 5 more minutes, handy for all sorts of things both while on the bottom and while ascending).
Dive planner: both have them, but I liked the NDL @ X depth now/in Y minutes and dive planner on my Cobalt much better than the one on my Petrel. What the Xeo does in this regard is an unknown for me.