AlphaSnake
...and that, kids, was the first time I sucked a dick for crack
Everything you've sourced are comparisons of European diesels...for an American buyer. We don't care for diesels here. The BMW's diesel and 4-banger is known to be better than others. Also, I get the feeling you're sort of hinting at something in your post about biases...but I won't get into it with you. Instead, here is an awesome comparison review:
Jaguar XE-S vs BMW 335i M-Sport by Motor Trend:
https://www.youtube.com/watch?v=-3YFTFLmcfk
And...
BMW 340i Review by Car and Driver:
http://www.caranddriver.com/reviews/2016-bmw-340i-test-review
Jaguar XE-S vs BMW 335i M-Sport by Motor Trend:
https://www.youtube.com/watch?v=-3YFTFLmcfk
And...
BMW 340i Review by Car and Driver:
http://www.caranddriver.com/reviews/2016-bmw-340i-test-review
I'd be careful about some of the advice you get in this thread regarding cars and such. Some are highly impartial to specific brands, or the cars they own, and often throw facts, figures, data, professional reviews, reports etc to the wind, in order to champion pre determined preferences. It's almost like console fanboy wars at times. I've also learnt that when some use terms like "garbage" or "trash" to describe cars, engines, brands etc that are otherwise globally revered or commended, you're sometimes best just ignoring such opinions altogether, as it's often little more than unhelpful hyperbole.
Regarding the cars you've chosen, luckily they're very popular choices which have tonnes of comparisons already made. These are the top ones on Google and YouTube, nothing cherry picked, just the popular one's that come up first, in the order they did for me. Please be aware, they may not all line up with your specic engine options. You might as well also search out some more for your own.
1. TopGear | Diesel triple test: Jaguar XE vs Mercedes C-Class vs BMW 3-Series
Conclusion.
2. AutoTrader | BMW 3 Series vs Jaguar XE vs Mercedes C-Class
Conclusion.
The BMW 3 Series wins out of the three, Jaguar in second place, Mercedes in third. For the reasons why, just watch the video.
3. AutoExpress | BMW 3 Series vs Jaguar XE
Conclusion.
http://www.autoexpress.co.uk/bmw/3-series/92761/bmw-3-series-vs-jaguar-xe
4. WhatCar | Group test - BMW 3 Series vs Jaguar XE vs VW Passat
Conclusion.
5. CarAdvice | XE 25t R-Sport v Lexus IS200t F Sport v Mercedes-Benz C250
Comparison Review
Conclusion.
BMW 3 Series takes first place, Mercedes second, Jag third. Read article for comprehensive comparison.
6. AutoMoto | 2016 Mercedes C 250 vs BMW 330i vs Lexus IS200t vs Jaguar XE R-Sport
Conclusion.
Lexus wins. In order of their preferences, Lexus, Mercedes, BMW and finally Jaguar. Watch the video for a better breakdown.
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Personal opinions.
Your car selection options closely mirror some of my own from a few months back. In the end, a few of the cars I narrowed it down to were the 4 Series Gran Coupe, 3 Series and the Jaguar XE. I actually test drove and compared all of them (though ended up with something completely different in the 3 Series GT M Sport, which I'd barely heard of before testing it at the garage).
Seeing as how the 4 Series GC nor 3 Series GT are in your list of choices, here's how I'd personally stack the final two that made both of our shortlists, based on my personal experiences.
Aesthetics - XE > 3 Series
Just find the XE looks a little sleeker and more sophisticated, though the 3 Series M Sport trim still looks very nice. The Jag's interior also looks a bit more luxurious, futuristic and less clinical than the BMW's more industrial look.
Interior - 3 Series > XE
Whilst I did think the XE's interior looked better, the BMW's was imo more practical and efficient. The cabin is roomier, there's more rear headroom and leg space, visibility from the rear is better, and the LCD screen and instruments are better positioned.
Ride - 3 Series > XE
The XE was a little nippier and sharper around corners, but I felt the BMW offered not only better feedback of the road, but a better balance between comfort and sportiness. The XE is a little stiffer and less forgiving, and doesn't eat up the road as well.
Gearbox - 3 Series > Jaguar XE
Even though both are brilliant and completely comparable (in-fact they might even be the same hardware wise), I still found BMW's set up was a bit more efficient and clever. The Jag's upshifts can pause a tiny bit longer before the next shift than the Beemer's, which feels more instantaneous in comparison.
Practicality - 3 Series > XE
This goes back to the roomier cabin of the 3 Series, on top of which it has the bigger boot as well, at 480 litres vs the XE's 455 litres. Also touched upon, it has a more comfortable overall ride too.
Engine - Depends
With the two diesel versions I tested, the BMW was quicker and got better mpg, but I'm not entirely sure how the US petrol models stack up. Based off of a quick googling, the 340i does 0-60mph in 4.6 seconds, and the XE 35t in 5.1 seconds. The 340i's mpg is 22/33, and the Jag's is yet to be announced.
Conclusion
If I had to choose between the two cars, in all honesty whilst I'd probably prefer the 3 Series (purely for practicality reasons), I'd actually just go with whatever was cheaper, or whoever offered me the best deal. They're both excellent, but as I said before, I ended up settling for the 3 Series GT M Sport in the end, and were I to pick a less practical option in this sort of price range, it would have likely been the 4 Series Gran Coupe instead of the 3 Series or XE.
Ultimately, the final advice I'd give is for you to just head to the garages and test drive all the cars you've shortlisted, however time consuming it may be. There is literally no better way to gauge your own preferences than that. Test them how you'd use them, e.g. the local routes, roads etc you use most, and also take along those who are likely to be the future passengers in your vehicle, whether in the rear or whatever, to gauge their thoughts as well (on rear comfort, space etc). The Garages might try to entice you to buy on the day with deals etc, but I'd hold out until you've test driven all your faves.