I currently own and gig both on a regular basis.
The Mesa wins on the feature set for sure. The DI is better and more flexible. The line out on the Fender that is affected by the master volume is annoying in many situations.
As mentioned above, the Mesa D800 also has a mute button, input pad, deep switch and the voicing control, in addition to a four band eq layout. Tho I'm not in love with the high mid band freq center. Obviously, the + model fixes that and a whole lot more.
The Rumble has a few presets that can be cool but aren't really my thing. I really like it's inherent voicing and like its frequency points on the preamp. It just sounds really good at classic sorts of bass tones. The lack of features are what annoy me for gigging purposes.
The Mesa tone maybe isn't my favorite but the features and flexibility are what I probably value most for gigging. I played an outdoor stage in Miami on Sunday that was, for whatever reason, very stuffy sounding. The first set was with the Rumble (and a separate DI to avoid overly screwing with my FOH signal) and I could not get rid of the high bass /low mid congestion. I switched to the Mesa and flicked on the deep switch and brought down the bass knob and low mid knob. It instantly fixed the stage sound. I played an outdoor wedding on Saturday where I preferred the Fender based simply on tone. Though it can be fiddled with, the Mesa is generally deeper and quicker/stiffer and more modern sounding.
So, depending on your tastes and priorities, either will serve you well. I bought my Fender as a backup to a Tone Hammer and wound up preferring the Fender. I got the Mesa to make up for the lack of features of the Fender.
I have my D800 listed for sale and am mostly thinking of getting the + model so that I can use one amp for all my cabs but the regular version has proven to be great.
The Fender sounds great and has proven reliable and plenty loud so really, I would figure out your priorities, money/tone/features to help make the decision.
That was a loonnggg post....