Summarizing features of bench vs handheld the most unique item in benchmeters remains the highest available accuracy and precision. Bench DMM that look like a bench meter but have features, accuracy and precision of a HH are a waste of space, IMHO, unless they are sold at a substantial discount pricewise.
In the past 10 years, built in trend capture has been a timesaver I wish I had, each time I truly need one I rig up my laptop for realtime data capture and plotting or setting the scope on roll mode, having that feature saves me setup time and I'd use it nearly all the time.
There are a few metrology grade benchmeters that would sell for $100 typically in the USA [ range $50-200 working, $300 with cal certificate FWIW] that would be worth having for the accuracy and precision, for any lab wishing so but can't justify the cost of a 34461a or similar. Those would be the HP3456a and HP3455a, both are DVM. The HP3457a is a full DMM, is about $200-500. The DC accuracy of the 3456a is overall better than the new 34461a. You can find spec sheets online.
There are many used non-HP metrology grade DMMs but the problem are spare parts to keep them working. What I did over 2 years was buy 4 3456a working, assuming some would die along the way. 4 years later, one died that I keep for spare parts or repair as needed, while 3 remain working and calibrated, and I paid about $100 for each on average, cal included.