Probably one aspect that many here are interested in, and on a slightly different tack (but still within the scope of this thread) is which of the two would be a better endorsement to have (given the choice of one, but not the other) in terms of securing employment in that first multi-engine job?
To that end, you'll find no real distinct dominance of one type over the other in GA charter companies, although there are probably more Barons than 310s about. Some companies operate one type exclusively, some companies operate both types. Either is a capable light charter twin, certainly when compared to other machines such as Senecas, Partenavias, etc. My thoughts are that a C310/340 endorsement is as valuable as a Baron/Travelair endorsement when seeking work - they serve to show some level of experience with a "useful" GA airplane, but neither is a deal breaker if not held by a prospective pilot...
From a technical standpoint and from my experience, the 310's superior ground clearance is a solid benefit on unsealed airfields, two-bladed Barons in particular are at risk on these. Also, my opinion is that the 310 has a nicer "ride" for passengers - the Baron feels worse in rough air and with it's lower cabin roof, I have sconed my noggin too many times in a Baron on turbulent days to be a massive fan.
The Baron wins with the utility door and operating simplicity of the fuel system (but the engineers hate the bladder fuel cells...), however a big issue with the Baron is that you never positively know how much fuel is on board unless it is full, or empty - the accuracy of the fuel gauging system is a nightmare. The 310 has vastly more accurate fuel quantity sensing, but requires more solid SA in order to manage the fuel system (not altogether a bad thing, as it does get one versed in fuel system management rather than the "fire and forget" selections on the Beech). Never seen a 310 without evidence of the "fuel dump" from the main tanks...
The new model Barons are a beautiful thing with their ergonomics and avionics and it is hard to beat the solid feel of a Beechcraft (but don't you just hate removing the cowls on them?).
So, they are good in their own different ways - it's a bit like a Ford vs Holden thing...