I have a PM1 in D2 and a 710 in M390.
Ergos -
The 710 is remarkable for how much blade it packs into relative to its handle - same handle but notably longer blade with more cutting edge than the PM1 (the PM2 has a tiny bit more blade but still shorter). PM is less efficient but I like the handle ergos and presence of a choil better.
The thumb studs on the 710 tend to snag on some of my pants pockets (but not on others) and they are a bit harder for me to find than the big Spyderhole on the PM.
710 rides more discreetly in pocket due to higher clip, PM is easier to access due to "high-rider" clip but more conspicuous. 710 is tip-up ONLY, PM1 is tip-down ONLY but PM2 is 4-way clip. I like the look of the clip on the PM2 less though. PM1>2 resulted in some slight ergo changes, so bear that in mind when reading the rest of my thoughts.
Blade -
Both are good cutters, 710 has a great point, fine enough for splinter picking or thread cutting but still pretty sturdy. PM has a slightly finer tip which I am more concerned about breaking. PM has a taller blade and higher grind, slight edge in deep cuts. Think I have a slight preference for the blade on the 710.
Locks -
I like the Compression Lock very slightly more for ergonomics of operation and reliability (no Omega Springs to possibly break). Axis Lock is a tiny bit harder for me to manipulate: the studs for operating it get caught on the meat of my palm occasionally. Compression lock is smoother and more flickable, Axis lock has stronger closing bias, maybe a bit too strong for me.
Finish -
PM has a very tiny bit of vertical play. 710 has no play at all (although the PM is older and has been used more). 710 has some grip-grooves machined in G10 but I don't think they are very nice (not attractive, don't add grip). Both have attractive, sturdy clips with no play. I like the way the liners on the PM are inlaid into the scales. Makes for a slightly thinner and more attractive knife, in my opinion. PM is slightly lighter overall. 710 has a full backspacer (feels like a cheaper plastic instead of G10 although I could be wrong) which keeps crud and coins out but the PM is easier to clean and blow dry.
Overall the 710 is really a classic design with a beautiful blade and well-deserved longevity in BM's lineup. The PM takes advantage of a few advances in design and technique (inset liners) which make it a bit more elegant. The 710 has a bit of a classic, sturdy-tool feel to me while the PM seems more high-tech, high-performance. If I can make a car analogy (I know, everyone hates them), the 710 is a muscle car, something like a Mustang with the new 5.0 while the PM is more like a rally car, maybe a WRX STI. Both are high performance but they take different approaches. I have been alternating them pretty much since I got the 710. I think I prefer the PM a little bit thanks to the smooth opening action, choil, and Spyderco hole but I also find myself picking up the 710 very nearly as often and appreciating how much blade it packs in an unobtrusive and usable package.